Where must a small unmanned aircraft's serial number be listed when using either standard remote identification or a broadcast module?

Why →Under 14 CFR § 89.110(b)(4) for standard Remote ID aircraft, and § 89.115(a)(1)(ii) for broadcast modules, the applicable serial number must be included on the aircraft's Certificate of Aircraft Registration (or provided to the FAA in a notice of identification before the operation). That registry entry is what lets the FAA and law enforcement connect a Remote ID broadcast to a registered aircraft and owner.

The trap →The declaration of compliance is the manufacturer's filing certifying the equipment design meets the Remote ID rule, and serial numbers do appear there. But the requirement common to both compliance paths is the registration listing. "Method of Compliance" names a different document entirely.

Field note →In practice this happens in FAA DroneZone: the registration form asks for the Remote ID serial number. If you move a broadcast module between aircraft, update the registration to match.