Undetectable Firearms Modernization Act This bill revises the federal statutory framework regulating the manufacture, possession, sale, import, shipment, delivery, receipt, or transfer of undetectable firearms. Current law requires firearms to be detectable by walk-through metal detectors after the removal of grips, stocks, and magazines. Specifically, firearms must be as detectable as a security exemplar (i.e., a piece of stainless steel that is 3.7 ounces and in a shape resembling a handgun). There are exceptions, including for firearms manufactured for or sold to U.S. military or intelligence agencies. This bill requires firearms to contain detectable material after the removal of all parts other than major components. It defines detectable material as material that produces a magnetic field equivalent to that produced by 3.7 ounces of stainless steel. The bill also revises and broadens the exceptions to include firearms (1) received by, in the possession of, or under the control of the United States; or (2) produced pursuant to a contract with the United States.