One thing you must watch out for. That is the so-called NIST number. The number by itself is NOT valid for traceability, according to NIST itself. If that is the information provided, you should request a copy of the specific NIST report showing the calibration of the lab's standards!
If the lab can't or won't provide the report (if they are claiming the NIST number), that is a red flag. If they provide the report and it shows calibration of some other item, then there is a broken link, and so no traceability. If they provide the first page and it shows calibration of the lab's standard then you should be OK.
Of course, if the lab's standard(s) have not been recalibrated in a few years or more, then again, that is a red flag.
Why do you need this info? Every cal lab in the US claims traceability through NIST. But the proof is in the documentation!