Never Say Goodbye (1956) - Rock Hudson, Cornell Borchers
Dr. Mike Parker departs California to speak at a conference in New York. A widower, he and daughter Suzy have a deal with each other to never actually say goodbye. She remains behind with Miss Tucker, her governess.
While Mike is having a drink after the conference, a caricature artist, Victor, comes to Mike's table along with a woman who plays piano at the nightclub, Dorian Kent. To their mutual shock, Mike recognizes Dorian as his late wife, Lisa.
Lots of drama and pathos unfold. It even has a small role for a very young Clint Eastwood!
You'll have to dig deep for this one, I can't even find a good quality trailer. I did find a really high quality 720p transfer 3 years ago, which may have been on Vimeo. I suspect it ended up suppressed as part of the 1950s Red Scare.