Yes, you can use FastML to get reliable ancestor sequences. I should note that the previous steps leading to this need to be performed very carefully, i.e., your alignment and tree need to be constructed correctly. The REAP protocol is pretty good at discussing the steps involved (paywall).
FastML itself can be annoying to use. Occasionally the server will not work (for whatever reason) and at other times very minor formatting issues in your supplied alignment or tree will cause it to break (and the server won't always tell you what the issue is).
An alternative is CODEML in the PAML package...although this is incredibly difficult to use and the documentation is
crap hard to interpret.
I can expand on the sequence of steps that I believe need to be taken for ASR (formatting tricks, programs to use, etc.) if required.