I honestly haven't read much Catholic-inspired Science Fiction, but there's certainly some with Catholic elements even characters that I have read.
A Canticle for Leibowitz by Catholic-convert Walter M. Miller comes immediately to mind.
And then, of course, Fr. Robert Hugh Benson's excellent Lord of the World.
One series I recall really enjoying when I read them years ago, but, definitely hesitate to recommend to Catholic readers is the Hyperion Cantos by Dan Simmons. It's a great Sci-Fi series which has a space-faring Catholic Church as one of its major factions. The horrific Priest's Tale is one that has stuck with me for a while. The first book is structured like the Canterbury Tales, with a group of individuals telling their own tales surrounding the strange world Hyperion and the foreboding creature called the Shrike.
The biggest caveat is that it doesn't necessarily portray the Church in a good light and there's quite a bit of obscenity, which has long prevented me from re-reading the series.
I'll be following this thread, as I'm always looking for good books to read.