Can I microwave polymer clay to harden it?
Maybe, but it's probably not a good idea.



For one thing, the package says not to do it. The manufacturer isn't just saying that because they want you to buy a toaster oven -- putting it in the microwave will result in burning.


  Because microwaves don’t heat evenly, parts of the mass will begin to
  cure and harden while others remain soft. Microwave ovens heat the
  inside of clay just as much as the outside, so as the cooking
  continues, parts of the mass will begin to superheat, melt, and
  actually bubble and boil while other parts of the polymer clay mass
  will merely begin to harden.
  Source: Can you Bake Polymer Clay in the Microwave?


Not only will that ruin the project, it releases fumes which at best smell terrible, and at worst can cause respiratory distress and damage. For health and safety reasons, you shouldn't microwave polymer clay on its own.



Some crafters do say you can microwave polymer clay as long as it is completely submerged in water. Basically, this is boiling the item to heat it and cure it, but in a microwave rather than on a stovetop.
Sources: [1] [2]

But, some crafters say you still shouldn't -- the quality of the final piece will suffer.


  Some people advocate using a microwave to boil water which contains
  the polymer clay. The problem with this is that ... boiling water
  never heats above 212°F (100°C) ... [below] the proper curing
  temperatures of most brands of polymer clay. While you may find that
  the item is hard after boiling, it will be incompletely cured and will
  be weak and easily broken. (This is true for stove-top curing as
  well.) Some brands of polymer clay will get an icky white residue when
  boiled... I think there’s room for experimentation there, but it’s
  very difficult to control the amount of heat the items would be
  receiving.
  Source: Can you Bake Polymer Clay in the Microwave?