Undetectable Firearms Modernization Act This bill revises the prohibition on undetectable firearms. Specifically, the bill prohibits the manufacture, importation, sale, shipment, delivery, possession, transfer, or receipt of (1) any firearm that, after removal of all parts other than major components, is not as detectable by walk-through metal detectors as the Security Exemplar (an object fabricated for the testing and calibration of metal detectors); or (2) any major component of a firearm that is undetectable by detection devices commonly used at airports for security screenings. The bill exempts from this prohibition (1) a prototype firearm for detectability testing; (2) any firearm received by, in the possession of, or under the control of the United States; or (3) the manufacture, importation, possession, transfer, receipt, shipment, or delivery of a firearm by a licensed manufacturer or licensed importer pursuant to an existing contract with the United States.