The most accurate way is to place the part in a closed circuit and wrap a coil around the part.  It's a direct measurement.  

Closed magnetic circuit?  Can you fill in a few of the steps?  I can see how you would calculate H (given measured current, turns and path length) but I don't see how B is directly measured.

I read a blurb that (I think) says that you measure the real power flowing into the winding, subtract the winding losses and assume the rest of the power produces hysteresis.  But that would ignore eddy current losses.  So I still don't quite get it.  Can you elaborate on how B (flux density) is measured with the setup you described?

Are you interested in testing a permanent magnet or a soft magnetic material?  Most permanent magnets are tested in (essentially) DC conditions so there are no eddy current losses.

A closed magnetic circuit in this case means you place the material in an electromagnet and close the poles on the material.  This forms a closed loop, as far as magnetics are concerned.

Here is a link to a website that shows a hysteresisgraph testing station (more appropriate for testing permanent magnets).  There is a sample in the electromagnet but the poles aren't closed yet.
http://www.magnet-physik.de/magnetic-measuring-technique_permagraph-c-300.html

We have a motor that commutates better when we place a steel tube around the OD of the field.  The electrical steel that the field is wound on gets well into saturation.  The extra steel from the tube increases the field strength enough to reduce the "armature reaction" that causes the problem with the commutation.  I'm thinking of replacing the steel tube with electrical steel to get the motor efficiency higher.  

I'd like to measure the flux density flowing through the field's laminations as I try different sized materials around the field OD.  I have a Gauss meter but its probe is a bit too thick to fit into the gap between the field and armature.  I thought of machining a slot into the field for the probe but then the probe would only see the flux density flowing through the air in the slot.  I was wondering how the measurement could be made without modifying the parts.

Unless I misunderstand your description, I don't believe a gaussmeter will work well for you.  The sensing element is large compared to the effect you are trying to measure.

Electrical steel will act as a lower reluctance path, but it might saturate earlier than the steel.  It's difficult (in my mind) to know for sure without FEA or actaully making the tube from electrical steel.