Not long ago, I posted a question asking what to do if my license plate had been lost or stolen. I got a well intentioned response stating that all I had to do was go to the motor vehicle office, report the lost/stolen plate, re-test my motorcylce for whatever, and then get the plate and re-insure my bike. (The current insurance just happened to be expired).
Although part of the above is indeed true, there is a couple of holes that need to be filled. Having just got my spanking new plate, I can report first hand on the process. 
What you have to do first is report the stolen plate to the police, which is no small feat. You’ll most certainly need a Taiwanese friend for this unless your Mandarin is at the native speaker level. Apparently, plates don’t get lost or stolen very often and the police are naturally suspicious. But that isn’t the hardest part. Noooooo…
First you have to find the police station house that takes care of your neigborhood. So I went to four police stations before I finally found the correct place (even with my TW friend!). Then you begin the report. Here’s where it gets tricky. About half-way through the input of info on the electronic form, the police said it’s not going to work because I’m not Taiwanese, and they have no process for reporting foreigner lost or stolen plates. Really! And they told us this after they had been plucking away at the keyboard for at least half and hour. Then the guy makes a few calls, and a couple other cops come in and between all of them, they figured out how to do it for a foreigner, much to my relief. Because, if I was understanding them, they were basically telling them that I wouldn’t be able to drive my bike again because they couldn’t formally report the lost/stolen plate.
Once I had the police report form, I was allowed to drive my bike to the motor vehicle office without a plate. And then I just handed the form to the guy who issues new plates, renewed my insurance and retested my bike for road worthiness. The new plate was NT$300.
It took the better part of the day to do this because of the cops. Although they were very well intentioned, they bumbled their way through the process. And I may have set a precedent, being the first foreigner in my city to file a report for a lost or stolen plate.
Now you know what I know. :bravo: