un-installing a microwave that does not have any visible top cabinet attachment
I helped a friend solve this very mysterious situation recently. Although every range hood microwave I'd ever seen or installed had screws run through the shelf above, this one had screws from the side, through the faceframe of the adjacent cabinets. The screws were covered with plastic caps set flush with the rails, so they were nearly invisible. I don't recall whether it was 2 or 4 screws in total.

Also look underneath any hinge leaves in that location.