There is a Serial.flush() command but I seem to remember that there are problems with it. The description in the reference pages says "Waits for the transmission of outgoing serial data to complete." which seems to me a waste of time if I understand it correctly as there will then be no data to flush.
After you have read the ID once you could read serial data and discard it until no data is available which would indicate that the card/tag had been removed.