Almost any moderate-tempo foxtrot would work. You probably want an instrumental; Frank Sinatra's voice wouldn't fit with Shakespeare. Here are a few titles. There are many more.
Laura (original version; the lyrics weren't written until after the movie made the song popular)
Moonglow
Pennies From Heaven
Smoke Gets In Your Eyes
The Way You Look Tonight
Why Do I Love You? (from Showboat)
These are all relatively old, but to someone born after these songs are new, they're "classical."