UPS will not pay a claim on NFA weapons . You are limited to FED EX air.
As your question concerns a few different aspects of shipping firearms through UPS, here's a breakdown of all the requirements: Handguns, as defined by 18 U.S.C. § 921,will be accepted for transportation only via UPS Next Day Air Services, specifically, UPS Next Day Air® Early A.M.®, UPS Next Day Air®, and UPS Next Day Air Saver®. (Note: UPS Express CriticalSM Service is not available for firearms). UPS accepts firearm parts for shipment, provided the part is not a "firearm" as defined under federal law; the contents of the package cannot be assembled to form a firearm; and the package otherwise complies with federal, state, and local law. (Note: Receivers or frames of a firearm, firearm mufflers and silencers are considered "firearms" and are accepted for transportation only if shipped in accordance with UPS's requirements for shipping firearms.) UPS does not accept automatic weapons, including machine guns, for shipment. Firearms (including handguns) and firearm parts are not accepted for shipment internationally. UPS ReturnsSM Services are not available for packages containing firearms. Follow These Packing Requirements Packages containing handguns must be separated from other packages tendered to UPS for delivery. All firearms are to be shipped in new corrugated packaging which meets the UPS Single Wall Box Strength Guidelines