How do I hang an OTS microwave without a cabinet above?
Over the stove microwaves generally have two main mounting points:


back bottom held up by a bracket attached to the wall
top front (on each side) using heavy bolts though the floor of a wall mounted cabinet.


The bracket mounting would work like any other. It is strongly recommended that all mountings of microwave units be attached to framing. While there are provisions for heavy-duty wall anchors (such as toggler type) these are strongly discouraged. You might consider opening the wall and adding a horizontal framing member if you can't find two studs. 

The upper mounts could go through a shelf in the same manner as a cabinet, but you need to ensure that the shelf is solidly mounted and can hold the weight. This would require supports just below the shelf and an angled support from the front edge of the shelf to a spot on the wall 8-12 inches above the shelf. Again, these supports should attach to a stud near each end. The shelf would also need to be the depth of the microwave.

Such a setup would give support comparable to a cabint mount.