When measuring such low values, I try to verify the measurement results with other devices, if possible. Then such values can be trusted.
Actually, sticking with your example that you raised, you just added a pointless measurement, because you had to measure the frequency of oscillation in-circuit anyway, with an oscilloscope.
Even if the tweezers provided any accuracy at such low nH values, you would have still had to measure in-circuit, to include all parasitics. Only then could your circuit have been trusted to operate at the frequency you required for ESR measurement.
I should also add, that you would have got a result precise down to the minimum individual turn that you could have wound, if you'd done the calculations on the core, so any frequency adjustments would have been by slight movement of the turns, or trimming the capacitor; again with an oscilloscope, not nH out-of-circuit measurements.