Just nice music, doesn't need to be authentic

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."

Nice suggestions . It might be worth mentioning that a 4/4 tune can be 24 bars per minute. Another 4/4 might be 50 B.P.M, which would probably not be suitable. Tangos now are also in 4/4 . I doubt if that would suit Shakespeare either. The Way You Look Tonight. Great choice.