This 1991 movie is a sentimental favorite of mine; at one point last year the DVD was going for $6.99 at Amazon, so I bit. (It's since gone up to $9.98 new, still a pretty good deal.)
Kenneth Branagh directed, and starred with his then-wife Emma Thompson. They both play dual roles. In scenes set in the late 1940s, they play composer Roman Strauss and his musician wife Margaret; in the opening scenes, Roman is about to be executed for Margaret's murder. In the modern-day scenes, they are private eye Mike Church, and the mute amnesiac Grace; Mike has been dragooned into trying to find out her identity.
The movie itself is a combination of straightforward mystery and supernatural mumbo-jumbo, which could have easily been a disaster; but Ken and Emma are at the peak of their powers here, and made it work for me. Things are helped along by good supporting performances from Derek Jacobi, Wayne Knight(!), Robin Williams, and Andy Garcia.
And Emma Thompson never looked more beautiful.