I assume this is a choke.

[MagicBus]

I think I have learned something useful here! Thank you very much!

 

[50AE]

You can do it with a scope, sig gen and a capacitor and resistor.
Connect resistor in series with L and C.
Sweep the sig gen until you get min signal across the LC.
That is your resonant frequency.

L=1/( 4 (pi squared)( F squared) C)

+1
The resonance method is the best one as far as I know.
Just make sure to get the Fres to be around 50-200Hz by altering the C value. If you intend to use the choke as a power supply filter one. At higher frequencies, the magnetic core losses will come into play. Of course it depends of the core type, but judging by your photo, this is regular silicon steel.

The higher value resistor you're using, the more precise will be the measurement. But then you'll need more voltage amplitude. I usually use a 10k resistor with a 10Vrms generator.