The procedure described by Miseremini is correct.
Sacred concerts were often held in the larger, more prestigious churches. The work had to be sacred, so as to be fitting for the sacredness of the space. Never secular concerts or events. So, an interesting example: Verdi's requiem was performed at San Marco's in Milan in a concert, not liturgy, since it was deemed too obviously operatic (even in those days!) for liturgical use. Nevertheless, it was a sacred work since it treated the Requiem Mass texts. Another example of a sacred work that was not fitting for liturgical use (due to its scale) was Beethoven's Missa Solemnis.
Most major French churches had regular organ concerts on Sunday afternoons and still do to this day.
And other magnificent works of sacred music that were not fitting for the liturgy may nevertheless have been written for devotional purposes, e.g. the many beautiful settings of the Stabat mater, the seven last words of Christ, etc. In these cases, the Blessed Sacrament did not need to be removed since the music accompanied a devotional practice and was not simply a concert. Of course, we can be sure that the "cultured" yet impious would have attended these devotions merely to listen to the music.