Mounting a microwave w/o the upper cabinet
The microwave doesn't "dead hang" from the shelf (very little would be able to support a microwave if that were the case). There's typically a mounting bracket you put on the wall and the cabinet holds the front up.



It should be noted that there's no way to mount it solely to the wall (this quote typifies all the answers)


  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.


The only way I've seen this done is either with a bracket or shelf under the microwave. (which limits the size)