The problem with measuring very small resistances is that the resistance of connections becomes so important relative to the resistance one is attempting to measure.
Put your ohmmeter on its lowest scale and, with fingers off the exposed metal on the probes, press the metal tips together. Now, by adjusting the pressure with which you press the tips together, you should be able to change the indicated resistance by a large relative amount.
Keep this in mind when you make your resistance measurements.
Don't forget that there is another set of connections where the meter test leads connect to the meter itself. These are generally banana plugs so wiping occurs with every insertion.
I'm trying to remember the Wheatstone bridge we used in physics lab at college. I seem to remember screw-down connectors for attaching the unknown but it's been a long time.
Rather than the error-filled minefield of resistance measurements, why not do it with weight? Weigh a small piece, weigh the coil and the math is the same as I indicated above.
Accurate scales are available and, if all fails, you can use a balance scale with measured quantities of water as the balance weights.
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