From Memory Alpha:

Of shooting this scene, James Darren says, “I was all choked up. They picked this great song, "The Way You Look Tonight”. All of the lyrics have a double meaning. I told Ira afterward, ‘From now on, whenever I sing that song, I won’t be able to think about this night, because I’ll never get through the song.’“

And Nana Visitor said she couldn’t stop crying.