Both of those cups are plain though, nothing special about them. I think the prices of them reflect that too.
I will call the number on Monday and see what the original retail was for it, that could help out a little as long as the name of the item from the catalog.
It could also destroy the value if the engraving wasn't done by Tiffany's. The blocks look a little crude so it is possible that someone else did them by hand.
I need to call them back with the sku number on the appraisal. They could not source anything with the pattern number, she said, its 14 years old at least, it most likely wont be in our system.
Here are more pictures. The blocks have a 3D effect as they are more raised on the corners to make it look like the blocks are coming out at you.
Hand chasing. With this method, silver is moved with a small pointed tool and a small mallet. It is much like what you'd do if you used a stick to draw in the sand. Silver is not removed, but designs are drawn in the metal with the tool using a small mallet. This method is also used to produce a textured background in the design.
There is a woman on Antiques Roadshow named Arlie Sulka. She was with the Tiffany archives and museum for 20 years or more and now is associated with Lillian Nassau, LTD in New York City. She can answer all your questions...
On my first reply the picture wasn't great and the blocks looked engraved. After seeing the second set of pictures and knowing that it is hand chased from Tiffany's I rescind my last comment.
I found this cup that was similar that had been on Ebay.