Thanks for you reply L&H. I don't think Ellie ever appeared "live" on stage with Mr Sinatra at any time. The "First 40 Years" was a tribute evening for Franks first 40 years in showbiz, with many star guests attending. Ellie never appeared on the show or as you say in the end credits, but she could have been in the audience during the recording of the show. It maybe wasn't Ellie at the end, but I think it might have been. 
I asked the same information on the IMDb Frank Sinatra message board, to no avail, as yet.
Frank Sinatra did appear as a band singer (with Tommy Dorsey) in his very first film, which was in an Ellie movie "Ship Ahoy".
What a great tribute Ellie and Fred Astaire were paid by the words of Frank Sinatra in the Thats Entertainment film, words which are absolutely true  
 
   
   
  
"My Tears Will Fall Now That You're Gone,
     I Can't Help But Cry, But I Must Go On"     
