I have an over-the-range microwave with wall bracket but no cabinets above. It is safe to hang it solely by the wall bracket or is the top cabinet to bolt it to a requirement?
If it matters, this is the microwave in question
I just hung a Whirlpool OTR microwave and attaching to the upper cabinet is a requirement. The lower bracket supports the back of the microwave, but does not keep it from rotating down. When you install the microwave, you put the back end on the bracket, rotate it up so that the top of the microwave touches the bottom of the cabinet, then hold it while installing the bolts from the upper cabinet. Two of us were holding it while a third installed the bolts, and it definitely would have fallen without us holding it.
I would install a shelf above the microwave so you can use it to hold up the microwave. I would then put some diagonal bracing along side the microwave to cover up the sides (not really meant to be visible) and make the shelf stronger by attaching it to the wall below the shelf. You would definitely want to hit some studs since my microwave weighed well over 50 lbs.
I have installed a couple of these. I don't see how it could possibly hang from just the wall without support from above. If you don't have a cabinet above it, then you need some creative ideas, like maybe constructing a shelf with diagonal bracing back to the wall. If you post a picture of the area, I'm sure the users on SE could come up with something.
I have been thinking a lot about this problem because I am in the same boat. I think I came up with a solution, but haven't tried it yet.
IKEA sells wall shelves with a hidden metal bracket. Basically you screw the bracket to the wall, slide the shelf over it, then screw the shelf to the bracket (mainly to keep it from sliding). They're really easy to install.
In theory you could install the wall shelf first, then follow the instructions for mounting the microwave and use the shelf as support instead of the upper cabinet. Then you also get some shelf space for some light decorative items or for food boxes.
The bracket already supports to weight all on its own because you just installed the bracket to the studs right. Now get an L bracket install upside down drill holes for microwave bolts. Now on wall side cut off the wall side of bracket so you only have one to two inches of bracket. Align those two inches to stud and drill holes in it and bolt in to studs, done.
Upper and lower support with minimal bracket view. Just need a carbon leaf to cut bracket and metal drill bit to make holes in bracket and good wall screws.