Undetectable Firearms Modernization Act This bill amends the Undetectable Firearms Act of 1988 to revise what are prohibited firearms to include any firearm: (1) 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 which, if subjected to inspection by the types of detection devices commonly used at airports for security screening, would not generate an image that accurately depicts the shape of the component. The bill modifies the definition of: (1) "major component" to include the barrel of a firearm only in the case of a rifle or shotgun, and (2) "Security Exemplar" to repeal the requirement that it be fabricated within 12 months after enactment of such Act. The bill exempts from undetectable firearms provisions: (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. (This replaces the exemption of any firearm that has been certified by the Department of Defense or the Central Intelligence Agency as necessary for military or intelligence applications or that is manufactured and sold exclusively to U.S. military or intelligence agencies.)