FIPS 140
FIPS 140 is NIST's standard for validating cryptographic modules, and anyone buying an HSM asks for the certificate first.
The standard arrived in 1994 as FIPS 140-1, was succeeded by 140-2 in 2001 and by 140-3 in 2019, the current version, which also follows ISO/IEC 19790. It defines four security levels, where higher levels demand more physical and logical protection, from pure software up to hardware that wipes its keys on intrusion. Validation is run by the Cryptographic Module Validation Program, a joint effort between NIST and Canada's CSE.
A certificate shows that a module was tested against the standard, not that the implementation is good. It says nothing about sloppy key handling in the systems around it. Public-sector procurement requires it anyway, which makes it one of the most read papers in the industry.