Arduino inductance meter using op-amp as comparator?
There are many ways to perform this measurement but when it comes down to nH accuracy every mm of trace length counts as adds 0.5~1 nH/mm.

The Op Amp must support the current and bandwidth required to drive the low impedance of nH ranges.

Another possible method is to use a linear LC oscillator , limiter and 8 bit binary binary counter to lower the frequency measurement.

http://www.falstad.com/circuit-java/e-eclosc.html