Do not leave the airport before filing a claim at the baggage desk. Write down the agent's name and employee ID number, and get the airline's direct baggage-claim customer-service phone number.

Call the airline every four hours for a status report. Getting results often "depends on how loudly and how often you complain, and how many managers you talk to," says John Hawks, executive director of the Consumer Travel Rights Center. The maximum liability for American carriers for lost luggage is $2,500 for domestic flights, $635 for international flights.