Microwave for meat/milk:
Some Rabbanim say that a microwave may be used intermittently for meat and then dairy and Pesach, after cleaning it. The majority consensus of Poskim however is that a microwave cannot be used for both meat/dairy even one after the other. Practically, one must abide by the latter opinion, as the former opinion does not take all factors into account and is hence inaccurate.
Cooking in a hermetically sealed container: In all cases, it is permitted to cook in a microwave food [meat/dairy] that is contained within a hermetically sealed container which does not allow any vapor to escape or enter. This applies even if the microwave has not been Kashered, and certainly if it has been Kashered in the method mentioned above. Some Poskim however discourage using the microwave in this method as it occurs that the hermetic sealing tears or opens during the cooking, which would then pose a Kashrus issue. It is therefore best to only use the microwave in this method after first Kashering it.
 See Piskeiy Tehsuvos 451/22; Sefer Hakashrus [Fuchs] 1/47-50 [pp. 48-49]; Nitei Gavriel 80/16; See also Hadarom Choveret 6 Nissan 5722; Kovetz Beis Ahron Yisrael 4/3
How does a microwave cook? A microwave is a rapid cooking element, which can warm and cook food much quicker than traditional cooking methods. Now, how does the microwave achieve its rapid cooking? The microwave does not use the heat of a fire or electricity to cook but rather cooks the food using radiation, or radio electromagnetic waves, which is projected from a vacuum tube and bounced off the metal lined walls of the microwave which penetrate the food from all sides. These waves hasten the movement of the water molecules in the food to atomic levels hence generating heat. [Heat is generated from movement and friction.] This form of cooking cooks the food much quicker than fire or electricity, as the radioactive waves hits the food equally in all areas and furthermore, penetrates the inside of the food molecules hence making the entire mass of the food an equal recipient of the heat. This is unlike fire or electric cooking which heats the external part of the food, and that heat then must travel to the inner part of the food in order to cook it. Likewise, this form of cooking only heats the actual food, as it does not actually send heat to the food but causes the food to heat itself up. Accordingly, all other areas and items of the microwave might remain cold, including the walls and certain plastic or glass containers which cover the food. The only way these items will become hot is if they are in contact with the food itself. The radio waves harmlessly pass through these containers into the food and do not cause any heating within them being they do not contain water molecules or other polar charge component. [See Hakashrus ibid footnote 100; See here for an educational video on how a microwave works. https://www.youtube.com/watch?v=kp33ZprO0Ck]
 Rav Yitzchak Yosef
 See all Gedolei HaPoskim mentioned in Hakashrus ibid and Piskeiy Teshuvos ibid, which include Rav Wozner, Rav Elyashiv, Rav Sheinberg, Rav Halbershtam; Nitei Gavriel ibid footnote 26 in name of Rav Neiman of Montreal;
 The reason: a) Although the walls of the microwave do not heat, nevertheless the steam and spills of the food inside make the walls absorb the food and hence it must be Kashered. [Piskeiy Teshuvos ibid; See Admur 451/41, Michaber 451/14, and M”B 451/81 that a vessel which absorbed the steam of an Issur requires Hagala] b) As there is a vent duct in the microwave that contains actual steam of food, and that area is not Kasherable. [Rav Neiman ibid
 As although the walls don’t heat up the microwave receives steam from the foods and hence must be Kashered.
 Hakashrus ibid; Nitei Gavriel ibid in name of Rav Neiman
 Pischeiy Halacha Kashrus p. 28; Piskeiy Teshuvos ibid footnote 106
 See Kovetz Mibeis Levi 3/22-9; Hadarom ibid; Beis Ahron Veyisrael ibid