The GE Spacesaver is probably your best bet.

We have (although it's still in its box) a Sharp Over-The-Counter microwave, designed for exactly what you're describing. (oh wait, I don't know its depth ...)

I cannot personally attest to it yet, but my fingers are crossed!

I have the Sharp mentioned above, in a box waiting for the rest of my kitchen to catch up.

I think will be what I want, but with some futzing. IMO it will not look right installed under a 12" deep upper cabinet. The unit is a bit over 15" deep overall, including the door. If you exclude the door it is still well over 12" - more like 13 1/2" if I recall correctly.

Assuming you want the stainless version, only the door is stainless, not the box. The box is painted silver, and is not a good fake for stainless. Its not attractive and IMO not intended to be exposed. However if you look at the installation instructions you will find that they show it installed that way.

I spent a lot of time with my KD and GC discussing how to handle this. we are pulling the cabinets out from the wall and putting some spacers for clearance so that the door can be flush with the cabinets and still open.

But none of it has been installed yet, so I can't show you any pictures.

A year or more ago somebody else installed one this way. He was doing custom cabinets and so made them fit right. He posted pictures, but I haven't seen him around for ages.