This is an issue I've done some research on (I sent the quotes to Sean, as I'm mostly just on mobile these days and didn't have time to format them correctly). The question of priestly confirmations is one on which all canonists and theologians are concurred: priests cannot validly confirm except and unless they have direct and explicit approval from the pope (including via indult). Priests cannot appeal to epikeia to validly confirm. I encourage people to read over the material Sean posted carefully. It is abundantly clear, even if it is disappointing.

In other words, it is a supplied jurisdiction which gives the priest the ability to validly absolve in necessity, but it is not a supplied jurisdiction which endows a priest to confirm validly. 

What allows a priest to confirm validly in necessity (i.e., as the extraordinary minister) is an express grant from the pope to exercise a particular power of Order (which is otherwise inaccessible).

Pohle-Preuss again: "the validity of Confirmation has nothing to do with the power of jurisdiction, but depends entirely on the character of ordination."

This has nothing to do with ecclesiastical laws, jurisdiction, etc.

The distinction between necessity supplying jurisdiction for valid confessions, but not supplying it in the matter of priestly confirmations seems to be this:

According to Pohle-Preuss, not even necessity can validate a priestly confirmation without the delegation of the pope, for the reason which follows:

“In extraordinary cases simple priests can administer Confirmation, but only with special powers granted by the Pope. This Proposition may be technically qualified as "sententia certa.
Proof. Hugh of St. Victor, Durandus, and other Scholastic theologians deny the right of the Supreme Pontiff to grant the special power referred to; but there is now no longer any reason to doubt it. Thomists, Scotists, Bellarmine, Suarez and De Lugo, all regard Confirmation administered by simple priests with papal autority as valid. Our thesis cannot be demonstrated directly from Sacred Scripture and we therefore have to rely on Tradition... [here follows a proof from the Eastern Tradition]...
b) In the Latin Church Confirmation, as a rule, has always been administered by bishops, and only in exceptional cases by priests.
This practice, which is far more in conformity with the dogmatic teaching defined at Trent, gained the upper hand in the West afther the thirteenth centutry, when Baptism and Confirmation gradually became separated by constantly lengthening intervals of time. The administration of Confirmation by priests was and is comparatively rare, but cases have occurred in every century since the time of Gregory the Great, though always with express papal authorization and with chrism consecrated by bishops. Since the Council of Trent the Holy see has at various times granted the right to administer Confirmation to Jesuit missionaries, to the Custodian of the Holy Sepulchre at Jerusalem, the Provost of St. Hedwig's Church in Berlin and other priests.
c) It is not easy to justify this exceptional practice in view of the fact that the validity of Confirmation has nothing to do with the power of jurisdiction, but depends entirely on the character of ordination.
A deacon, for instance, could not validly administer this sacrament even with papal permission, whilst, on the other hand, a heretical, schismatic, suspended or excommunicated bishop can do so even against the express command of the Pope. How, then, is it possible for a simple priest to confirm validly, if the papal permit does not supply the lack of episcopal consecration?
Various attempts have been made to overcome this difficulty.
Some theologians have assumed that the papal delegation is not a mere extrinsic permission but implies an intrinsic perfectioning of the character of ordination by which the delegated priest receives the episcopal character. Others hold with Suarez that the papal authorization merely gives to the delegated priest a higher extrinsic dignity which, together with his sacredotal character, suffices to enable him to administer the Sacrament validly. Both hypotheses are unsatisfactory. A simpler and more effective solution is that devised by Gregory of Valentia. It was the will of Christ, he says, that both bishops and priests should be empowered to administer Confirmation, the former as ordinary ministers of the sacrament by virtue of the episcopal consecration the latter as its extraordinary ministers by virtue of the priesthood, leaving it to the pope to determine the manner of exercising this latent power."

Pohle, Joseph, Ph.D., D.D.. The Sacraments: A Dogmatic Treatise. Trans. Preuss. 1917. Herder: St. Louis. Pp. 310-13

Thank you for these quotes, Sean.

Although I appreciate some may say that there are no good bishops from whom to receive this sacrament (which I, being aligned with RCI/IMBC, would disagree with), all that remains to be said is: Fr. Arrizaga's confirmations are invalid.

I agree that delegation seems to be necessary for a priest to validly bestow Confirmation.

Now, there are some traditional clergy who take the next step and conditionally confirm anyone who has been confirmed by priests in the Eastern Rite.  But the Eastern Rite priests have the proper delegation, right?

There are many people in our area who were confirmed by an old Byzantine priest before he passed away.  Some traditional clergy seem to have no doubt about it's validity but others seem to question it.  That is why I ask this question.

I never knew there were some who doubted the validity of Eastern rite confirmations.  

What is their reasoning?

The quotes above which were supplied to me by Mithrandylan contained an omitted historical discussion regarding confirmations in the Eastern rites (omitted because they were not directly relevant).

Now I am curious to read it.

Is the objection regarding Eastern rite priestly confirmation something along the lines of the papal delegation not being particular to specific priests (ie., they are saying a tacit, inherited delegation does not suffice)?

In lieu of doctrine, common sense tells me there should be no doubt, since centuries of popes haven’t seen the need to intervene/correct whatever the alleged problem is.

I never knew there were some who doubted the validity of Eastern rite confirmations. 

What is their reasoning?

The quotes above which were supplied to me by Mithrandylan contained an omitted historical discussion regarding confirmations in the Eastern rites (omitted because they were not directly relevant).

Now I am curious to read it.

Is the objection regarding Eastern rite priestly confirmation something along the lines of the papal delegation not being particular to specific priests (ie., they are saying a tacit, inherited delegation does not suffice)?

In lieu of doctrine, common sense tells me there should be no doubt, since centuries of popes haven’t seen the need to intervene/correct whatever the alleged problem is.

I myself am confirmed through the Byzantine Rite but never really questioned it's validity.  My family went to the Byzantine Liturgy for 2 years when I was 6-8 before going back to the novus ordo.  During that time I received my First Holy Communion, First Confession and Confirmation all from the Byzantine Rite priest.

Recently I have met some traditional people who told me that Bishop Sanborn (I think?..don't quote me on that) and several other sede priests they correspond with say that conditional Confirmation is necessary when someone has been Confirmed through the Eastern Rite.  I brushed it off but this thread made me think of it again.

Bishops definitely are the norm in the Latin Rite, but priests often bestow Confirmation in the Eastern Rite even from hundreds of years ago I believe?  If it wasn't for the fact that my confirmation was through the Eastern Rite I probably wouldn't even think about these questions.

Canon Law tells us that "the salvation of souls is the highest law".  Canon Law also says that laws don't apply in the face of "grave inconvenience".  Mix this with the fact of Pope Pius XII's papal indult and with the ever-growing rift in the Trad world, where Sedes, Resistance, New-sspx, etc don't get along at all, and you have the recipe for the laity to have a VERY DIFFICULT time trying to get confirmed.

I see no problem with Fr Arrizaga's logic.  Not only do Trads have to fight a culture/economic/political/religious war against God's enemies but also have to navigate mini-cινιℓ ωαrs in Trad land.  These are desperate times which call for desperate measures.  Canon Law and the Church are meant to HELP the faithful get graces, not put up barriers.

Had Pius XII (the last quasi-Orthodox pope we've had) not issued his papal indult, i'd say the argument was iffy.  But a papal mandate seals the deal, in my opinion.

If a couple can marry themselves, or seek some random priest to bless the marriage, after waiting only 30 days, why can't a priest confirm children/adults who've been waiting YEARS for such an important sacrament?  Even if all the Trad bishops got along (which they don't at all) there's just not enough to provide this sacrament on an annual or semi-annual basis.  The case of necessity is glaringly apparent.  God bless Fr Arrizaga.

'Accordingly, the Supreme Pontiff does not add a new intrinsic power to the priestly character, but causes the priestly character to extend itself to some act which itself can be performed by a superior power; just as the ear, while listening through the telephone, does not receive a new species of power or act, but extends itself to the object which itself had to be presented and adapted with the help of the instrument.'

Hugon also concludes that delegation IS necessary.

Pius XII's papal indult isn't a delegation?  Of course it is.

According to Pohle-Preuss, not even necessity can validate a priestly confirmation without the delegation of the pope,

Such a delegation exists...

Where such a situation still obtains, that is, where the priest in question is parish priest in all but name, the new power of administering confirmation will be enjoyed by the priest in charge.

Trad priests effectively act as parish priests because parishes/lawful authority don't exist anymore.  Trad priests are parish priests "in all but name" in a practical sense.

"The extraordinary minister [of confirmation] is a priest who, either by the common law or by special indult of the Apostolic See, has received the faculty to confirm. The following have this faculty by law: Cardinals (Canon 239/1.23), abbots and prelates nullius, vicars and prefects Apostolic. With the exception of the Cardinals, these clergy cannot validly make use of the faculty except within the limits of their respective territory, and during their term of office only.
[...]

Here again is a mention of an indult, which exists.

Persons who have by law the power to confirm cannot delegate that power to a priest, for as we saw above, the Code does not grant bishops the faculty to delegate a priest to give Confirmation, and besides there is no question here of delegating jurisdiction but rather a power of orders. No power of orders delegated to a person or annexed to an office can be committed to another, unless this is expressly permitted by law or by indult (Canon 210). When necessary, the Holy See grants bishops and others (vicars and prefects Apostolic) the faculty to delegate a priest for the conferring of Confirmation (emphasis added)."

Again, "unless permitted by law or indult".  Or "when necessary".

What did the Japanese Catholics do during the centuries of not only no bishops, but no priests?  Did they have some type of non-sacramental confirmation?  Since the faith not only survived but actually grew because the children did not abandon it, let’s have a look!