Installing OTR microwave with 15" deep cabinets
The simplest and most cost effective solution is to use a wood frame. The frame can be painted or stained to match the cabinets or wall.  Most of the OTR microwaves I have installed have a metal track at the bottom that screws to the wall first that the microwave hangs on and two screws at the top that connects it to the upper cabinet. If this is the case you could recess the frame to better conceal the lumber.