It would be wonderful indeed if the footage of that scene---which takes place immediately before the Lamento di Federico---could be located, but I think it's a very long shot indeed. After all, not even the cut scenes from
The Great Caruso have ever emerged.
In the case of Serenade, however, we do know what happened in that missing scene with Kendall and Damon. For copyright reasons I can't reproduce it word for word here, but you're right: it was an important scene---and a well-written one too.
In it, Kendall visits Damon in his dressing room just before his performance in L'Arlesiana. She tells him that she'd tried for months to find him in Mexico "to make amends" for her mistake in abandoning him. When Damon tells her that he's married now, she accuses him of doing that just to pay her back. He then angrily retorts that it had nothing to do with her---to which she replies, "Can you touch me and tell me that?" Realizing that Damon is unnerved by her words, she then delivers her parting shot: "It's not over, is it? ... Why lie to yourself? It'll never be over."
Damon is left standing alone "motionless."
Quite a dramatic scene!
If you'd like to know more about how the screenplay differs from the released film, there's a detailed post
here that you can read.
"Serenade" has a missing scene, which seems vital to the rest of the film. Found this photo, and wondered if somewhere in a vault this scene could be found, and returned to any future DVDs.