Bit more to this for European pilots who have a FAA certificate based on their foreign (e.g. European license).
See this document from the FAA on the process:
http://www.faa.gov/other_visit/aviat.../info08012.pdf
I realsie that some of you will complain that having the Euro license removes the need to comply but this FAA document makes it clear that you need to get the replacement FAA certificate if you are acting as PIC using that 'based on' FAA certificate.
I read the FAA document but on my FAA based on license it says:
"Based on and valid only when accompanied by UK pilot licence number XXXX. All limitations and restrictions on UK pilot licence apply".
My UK PPL is endorsed as proficiant hence my FAAbased on is the same.