I've used two different microwaves and both do the same thing, but it only does this at the initial start up. I checked the amperage while the microwave was running, and it's only drawing 10.8 amps. I even plugged a hair dryer in the same receptacle as the microwave and ran both loads for 5 minutes and it did not trip the breaker and it was drawing 19.7 amps.but once again after a few starts of the microwave it tripped the breaker. I have no clue what the issue could be and again this is two different microwaves.

Check for loose connections on the breaker, and check the buss the breaker plugs onto. Could be a bad breaker, swap with another 20 amp breaker, and see how it does.

A microwave must have an initial high load or, as suggested above, you have loose connections in your breaker box. I would not just check the breaker that is tripping, but all of them. The ones on either side could be getting hot and causing the one that is tripping to be more sensitive. When one is loose it's a good bet that all of them need tightening. They get loose over time, and this applies to all wiring connections, including the ones in your receptacles which will cause a fire fairly easily without ever tripping a breaker until the fire is burning. I had wires in my house burn the insulation eight inches or more from the receptacle and destroy the receptacle from loose connections. It happened in several switches and other receptacles, too. Go around your house and check all of the connections. It's very good fire prevention, too. You should check this out: Powerbox | Powering Progress | Power Solutions For Solid State Lighting | Inrush Current