Anchor's Away was a really sweet movie that earned him an Academy Award Nomination. From Here to Eternity was probably the best known one and Kings Go Forth was a romantic war film, if there is such a thing. Guys and Dolls is a cute romantic comedy type film and Young at Heart with Doris Day is really great too.
Some of the most romantic films Frank Sinatra has appeared in include It Happened in Brooklyn, On the Town, The Tender Trap, High Society, Pal Joey, Guys and Dolls, Can-Can, and Marriage on the Rocks.