I remember doing this as a kid. To measure inducance all you need is a AC step down transformer to provide 6 to 12 or so volts. A fillimant transformer is perfect. Connect the inductor in series with a resistor, low ohm, somewhere between 1 and 10, depends on the inductor, 10 or so watts. Apply AC to the circuit, then use a multimeter to measure the AC voltage across the inductor and also the resistor, write down both readings. Then disconnect it from the power cause it will be getting warm. You play around with the resistance value to get both readings about the same, just more accurate that way.
Then we use maths. We know the value of R, our resistor, and we can work out the circuit current (I) with I=V/R, V we measured across the resistor. Once we know I, and V across the inductor, we can work out its Impenance (XL) at the AC frequency. XL=V/I.
Once we have that, we work out inductance with L=XL/(2*3.14*Hz). Hz is the AC frequency, depending on country, 50 or 60Hz.
I'm pretty sure that maths is right, someone tell me if its not. Yeah I should have spent more time playing sports as a kid!
Glenn