Simplest calculation for L is just Vac across the coil and Iac through the coil. A slightly more complicated calculation accounts for the coil DCR to extract the inductance from the measured impedance. Try to apply the expected AC voltage across the inductor. Try not to use too high a test frequency, otherwise the shunt capacitance of the coil will modify the impedance - the first coil resonance frequency will indicate what is too high.
I used either an Omron G2R or Finder 40 series or similar style relay, and just cut away the contacts and top casing, and left the base and coil terminals, as I need a small footprint. I do have lots of pot cores and formers, but thought I'd try the relay coil. The DCR is in the datasheet.