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Googling for “precision current clamp” took me there:

There is no mention of lower limit of its range, but many clamps seem to start at 10-50 mA. Even the ones for oscilloscopes. Maybe there is so little magnetism involved in that little currents, that it would cost you arm and a leg to measure just a couple mA:s.

How about using existing cabling as a shunt with mooshimeters precision voltage input.. Specs say that it would have about 15 nanovolt resolution at 100mV range. It might need some calibration and math to give real values, but at least differences in current would be obvious from the start..

But if your quest for precision current clamp stumble upon some better tool, then i am also interested..