How can I calculate a Joule Thief
The typical conventional Joule thief can power a LED at 50 to 70 milliwatts, or about 20 milliamps at 3.3 volts.  The output can be shunt regulated by a 5.1V zener, and if your uC uses 50 milliwatts, for example, then the JT will put out enough power.  If you need more, then it can be made more powerful, and a zener and feedback can regulate it so that it wastes less power.   One example is here.  See my blog for more.