If either you or the FAA objects to the judge's ruling, you
or they can appeal to the 7 member National Transportation
Safety Board. Their ruling is final -- there is no appeal.

I thought you could take it to Federal Appeals Court...

http://www.kscourts.org/ca10/cases/2001/09/00-9500.htm

....and thence to the Supreme Court, although I don't think SCOTUS has
ever accepted such a case...