Airport Emergency Reimbursement Act of 2003 - Amends Federal aviation law to provide a credit to an owner or operator of an airport that allows the Director of the Federal Emergency Management Agency or the head of a State or local agency to utilize the airport to respond to a disaster or emergency. Allows application of such credit toward the non-Federal share of allowable project costs for projects carried out under the airport improvement program. Declares that such credit shall be in an amount equal to the revenues that the airport lost, including operational costs that were incurred by the owner or operator, during the period of such utilization.