Multifunction measuring instruments all have limitations and devices dedicated to such 'individual' components tend to be far more accurate. For 'small' measurements this is particularly noticeable and inductors as well as capacitors are commonly notoriously difficult to measure using 'broadbased' test equipment like your tweezers.
One relatively easy method (assuming you have the facilities and equipment i.e. accurate frequency counter) is to make a small LC oscillator with a calibrated capacitance and add the inductance to it - thereafter apply the relevant formula to derive the 'C' as the factor.
