We have an old Jenn Air that has a regular grill on one side and a flat cast iron grill on the other side, We can still use the flat solid grill, but it needs to be replaced (over 50 years old). I just measured and it has a very small lip all around it. It is 19" x 101/2" .Underneath is the coils to heat it up.Would the one shown on your site work?

It looks like this might fit. Please double check to make sure the 10-3/4" width will fit where your original was 10-1/2" This piece is manufactured for use on top of a grill grid, but should work for you as well. It is cast aluminum with a non-stick coating. It will be a little different than your original cast iron griddle, but should get the job done. Please let us know if you try it out and how it works. We don't get many 50-year grills around here!