Taking an extension cord from your home you can check the microwave by unplugging it from the RV and see if it works from the extension cord at home. If it doesn't work then, the microwave has a problem.
Some TV's will allow you access to the 120 volt AC plug. If you can get to it, try the same thing with the extension cord and see if you can get it to work. Make sure that your ignition switch is in the right position as some vehicles have ignition switch interlocks to the TV.
These tests cost nothing and they can at least tell you if your appliances are bad without paying an electrician.
Once you have the microwave unplugged, then you can check that outlet with any other 120 volt appliance to check for power.
Basically before you call an electrician, you can safely check things yourself.
If all of the outlets have power, and you cannot get the TV or microwave to work using a separate extension cord, they will both need to be repaired or replaced.
It is still a good idea to find out what caused the problem which MAY be impossible now if it was caused by a brief power surge.