I need to find a 12x17mm gem for setting on a billfold. I bought the billfold on eBay and the gem is missing. I saw a photo beforehand, but didn't notice. Ugh! I think a cabochon is what I am looking for and it will probably have to be 12x16mm correct?
The mounting you describe sounds like it would accommodate a cabochon which is domed on top and flat on the back. Standard settings are made to fit calibrated stones and are the type of settings typically used in finished goods like the one you purchased. If the billfold you purchased is handmade though, it may also have a custom setting which would then fit only the custom cut stone it was made for.
If it is a standard setting, the calibrated size oval cabochon closest to your measurement is 18x13mm. Browse the selection of faceted gems and cabochons to see if there is a stone you like.