Hi,
One way is by measuring the inductance and looking for a drop for some current level.
Since the material becomes magnetized when the current flows and the magnetic
field gets stronger as the current increases until saturation, you might use a
hall effect sensor to detect the field near one of the poles and as you apply
more and more current the field will keep increasing until it nears saturation
and then the field will either stop increasing or start to increase much less
for the same increase in current.
Some of the linear hall effect sensors are not that expensive. You'll also need
a small power supply to power it.
There is a problem however when trying to saturate a material that does not have a
closed magnetic path, and that is that the reluctance of the material is very low
but the reluctance of the air is not, and the air becomes part of the magnetic path.
The combination of the magnetic material and the air means the material may look
like it takes a huge huge current to saturate because the magnetic properties
of the entire construction (air and material) appear like a very linear choke because
of the linearizing effect of the air. In fact, air gaps are often introduced into power
chokes for that very reason: to make saturating harder to do (require more current)
and with a huge air gap such as that which would be the same length as the material
itself, i would think it would take a huge current to see anything like saturation.
On the other hand, with a material that can fold back onto itself such as a piece of
material that forms a closed loop, that may saturate quite easily as most of the field
would be concentrated inside the material.
I guess this also says how to minimize the current needed to saturate the material:
construct it into a closed loop with as little air gap(s) as possible.
This reminds me of an interesting experiment i did once...
Take a regular toroid core and wrap some turns of wire around it, then measure the inductance
and the dc current that it takes to saturate it or at least start to saturate it.
Take the turns of wire off,wrap the core in a clean rag, put that into a vise, tighten slowly until
the core cracks. Take the pieces out trying not to loose any, then glue it back together with super glue.
Put the same number of turns of wire back on.
Measure the inductance again and the saturation current, and note that the inductance
goes down and the current needed to enter saturation goes up. The reason being that
the cracks filled with glue now act as gaps, and the way most cores break like this there
ends up being four gaps, and even that thin glue layer four times over creates air gaps
that are effective enough to dramatically change the characteristic of the core.
You can also glue two of the four pieces back together and then vary the gap by
placing the two halves close together, which means two gaps will be larger.
Perhaps some hot glue would help keep them together just to make the measurements.