(Sorry folks, I'm on west coast time and I work late.)
Guys, I don't think there are any experts when it comes to anodizing with microwaves, cause nobody does it. I'm afraid you're stuck with a materials engineer who studied electro chem in college and who fooled around with microwaves and their reactions with materials for a spell. Don't ask.
There is a rather large difference in the frequencies. 60 Hz for household current vs 2.4 GHz (2,400,000,000 Hz) for microwave radiation. This makes a big difference in what can happen.
When you Anodize, you are depending on OH- ions (hydroxyl ions) to migrate to the surface of the Ti then be reduced by the positively charged Ti, forming water and TiO2. With a frequency of 60 hz, you have a positively charged surface for 1/60 seconds. That gives time for the hydroxyl ions to migrate to the surface of the Ti and react. The reaction is one way, so when the Ti becomes negative, the oxide layer remains. It could work.
With a frequency of 2.4Ghz the surface changes polarity every 1/2.4x10^9 seconds. the polarity would shift so fast that IMO the hydroxyl ions would not have time to migrate to the surface and react. The limiting factor would be hydroxyl migration rates rather than reaction rates. I got no data to prove it, Might get it if I worked a few hours in a university research library to look up anion migration rates in solution.
IMO it ain't a happening thing.
In edit I removed these statements because I forgot a conversion factor and the numbers were bogus. Sorry, I was moving too fast.
(Moreover, the wavelength of a 60Hz wave is a couple of miles in length. That means the entire piece of metal will be positive during that time period. ) (And the wavelength is about 1/2inch. That means that If you wanted to anodize a 3" piece of ti, the enitire piece of Ti would not be positive at once. And action. )