N.B. a coil on its own tends not to have any (useful) frequency response, unless you are hunting for things caused by the interactions of inductance with internal parasitic capacitances. Are you intending to use it with a capacitor to make an LC circuit?
> Is it as simple as sweeping a coil with sines with an arbitrary generator while the scope is across the coil on FFT mode?
I believe so, just make sure your scope is measuring something useful (eg current into the LC circuit) and ensure that you are aware of whether or not your siggen changes amplitude when you change frequency (depends on the design/quality/age).