Connect a known capacitor so that you have an LC tank loop. See what ringing frequency it gives after an electrical jolt of any kind.
This will work regardless what is the ohmic resistance in the loop. You can calculate the henry value from the frequency and capacitor value. Keep in mind the capacitor value may have a wide tolerance.
2.
See what time constant results after you hook up a low ohm resistor across its leads, then send current through for a moment and then disconnect the supply. The current takes about five time constants to drop to 1 percent of initial current. The inductive time constant is L/R.
To use this method you must take into account the ohmic resistance in the windings.
3.
There ought to be a way to use phase shifting as a way to calculate henry value. I'm not sure just what setup will do this. This method will require taking into account the ohmic resistance of the windings.