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1)If a microwave oven's Kashrus is compromised, according to many Poskim it can be Koshered, as follows:

The microwave  should be totally cleaned.

 A cup or bowl of water should be placed inside and the microwave turned on for approximately 10 minutes.  The bowl with water should then be placed in a different spot in the microwave, and the microwave should be turned on for an additional 5-10 minutes.

If the microwave is being koshered from a non Kosher usage (as opposed to just from milk and meat) 24 hours should be waited before doing the above procedure.

If there is a glass plate in the microwave, a Rav should be consulted regarding if it is able to be Koshered, and if so, how. (See Piskei Teshuva Orach Chaim Simon 451 for more on this topic)

2) If a Chometz microwave is being koshered for Pesach (something that should ideally not be done unless extremely necessary) , the food warmed up in it should be double wrapped, even after Koshering. (See Shu"t Teshuvos V'Hanhagos Vol. 2 Siman 212 and Yalkut Yosef Vol. 5 page 360)

If there are any plastic components on the inside surface of the microwave, a Rav should be consulted to determine if it is possible to Kosher.

If the microwave has a browning element or is a convection oven, it needs to be cleaned, and then turned on to its highest setting for 45 minutes, in order to reach its highest heat and thus render the oven Koshered.

There are certain models that do not reach the required temperature to effect a proper Koshering, so it's important to check with a Rav regarding your particular model.