I use Mothers Mag and Aluminum Polish. It is made to use on all metals. It works remarkably well. I have used it many times throughout the year to clean up my SS watch. A couple weeks ago I whacked the watch on a metal door frame. I was totally bummed because it left marks on the glass that I thought were scratches. While polishing the SS, for kicks I tried some polish on the glass (figured it didn't matter if I made it worse as I was going to replace the sapphire glass). Turns out the Mothers took off the marks on the glass. There is no sign that I did the damage. I think it must have been some paint that transferred from the metal door frame to the glass. I also figured I would take off some of the screen's coating, but there is no sign it did so. Water beads consistently so the coating is either still there or had already warn away.
Anyway, bottom line is I have had great success with the Mothers Polish.