Moser from ReiBot has developed a simple project for using an Arduino along with an LM399 and several discrete components to measure inductance. He says:
So you need to make or measure an inductor, but you don’t have an oscilloscope or signal generator? Measuring inductance with a handful of cheap common parts is certainly possible. I’ve verified this method is accurate with a scope from 80uH to 30,000uH, but it should work for inductors a bit smaller or much larger.
You can get more project details as well as the Arduino code (in a PDF) at ReiBot.org.