If you are an end user of the hardness tester, then you should have a calibration provider accredited to ISO/IEC 17025:2005 come calibrate the testers for you and as Tow pointed out that should be fine.
If you are a test or calibration laboratory and are seeking accreditation, then first step is to get a copy of ANS/ISO/IEC 17025:2005 and read it.
Accreditation is down the road aways if that is the path you need; however it is certainly achieveable.
As has been stated, accrediting bodies (ABs) are the ones that conduct the assessments and issue the accreditation. The link provided is good but for accrediting bodies is incomplete (not under Jim's control), as there are six recognized ABs based in the U.S., they are: IAS, NVLAP, A2LA, ACLASS, L-A-B, and PJLA, all for both testing and calibration.
Now, technical standards also come into play for hardness and conductivity. Those will likely be ASTM for those two.
A little more information about your need and usage will help us help you better.