Tool or Process to check for AES-NI support on processor?

On Linux systems, do:

grep flags /proc/cpuinfo

This will give, for each CPU core, the list of what that core can do. The AES-NI instructions are there when the flag "aes" appears in the list of flags. See this page for a list of possible flag values.

On macOS, do:

sysctl -n machdep.cpu | grep -i aes

If it doesn't find anything, this machine doesn't have AES-NI.

For Windows, see this question on SuperUser.

I'm not a low level hardware person any more, but an example from this post regarding a FreeBSD implemention shows you can grab info from Features2:

Features2=0x29ee3ff<SSE3,PCLMULQDQ,DTES64,MON,DS_CPL,VMX,SMX,EST,TM2,SSSE3,CX16,xTPR,PDCM,<b17>,DCA,SSE4.1,SSE4.2,POPCNT,AESNI>

On Windows systems, you can use free console tool "Coreinfo" from Sysinternals