Sorry to hear of your troubles.

If you do carry an AMEX esp. Plat or Cent first call should be to them. They will cancel the card, and in most cases contact the hotel on your behalf and arrange for payment in the absence of your physical card. If you have a leisurely enough breakfast your replacment card will be waiting at the desk for you when you are finished. Love AMEX or hate them, they do this very very well IMHO.

Cheers.