Electronic – How to choose the right frequency when measuring coil inductance with LCR meter

Arguably, the easiest way is to just measure it:

      +--------+          
      |        | 
      |      [50R]
      |        |
      |       [C]
    [GEN]      |
      |        +------+
      |        |      |
      |       [L]  [SCOPE]
      |        |      |
      +--------+------+ 

With \$C\$ known, adjust the generator's output frequency for a peak across the scope, then determine the reactance of the capacitor with:

$$X_c=\frac1{2\pi fC}$$

Next, since the reactance of the capacitor and the inductor will be equal at resonance, (the frequency at the maximum amplitude of the peak on the scope) solve for the inductance with:

$$L=\frac{X_c}{2\pi f}$$

Both equations can be combined:

$$L=\frac{1}{(2\pi f)² C}$$

You may need to adjust the value of the \$R\$ in order to get a nice peak.

Your RLC meter assumes that the parameter you select is the only significant attribute of the item being measured, so when you tell it to measure R it assumes that the stepper motor coil is a pure resistor with no inductance or capacitance. In reality the coil has significant inductance which will increase the reading. At 10kHz the coil's impedance is mostly inductive, so the L reading should be fairly accurate but the R reading won't be.

For PWM current control the inductance value isn't critical - it just has to be high enough to keep current ripple down to an acceptable amount. However the resistance value is critical, as it determines the average current through the coil. At high frequencies the resistance will increase due to skin effect, but in the frequency range you intend to use and with the small diameter of the coil wire, its AC resistance should not be much higher than your DC measurement.

Ignore the RLC meter's AC resistance measurement. The DC value should be close enough. Use the lowest available PWM frequency that still maintains continuous current flow in the coil at the lowest PWM ratio you intend to use.