This obviously requires a network analyzer with dedicated computer software.
You could roll your own and perform manual plots if you are only interested in the |Z| component, with a sinewave oscillator, a good (flat frequency response) audio amp, a wideband current probe (or sampling resistor) and a dual channel scope.
Stepping the frequency, take voltage/current readings, write them in an Excell spreadsheet and perform the conversions and perform the plot there.
If you are really resourceful and have the patience to do it, you could also measure the time delay between the reference voltage waveform and the current waveform. Convert it to electrical degrees by multiplying such delay by the test frequency and 360. Keep note whether the current's phase advances or delays with respect to the voltage waveform, and apply the proper polarity's signs to the phase readings.
Write everything down in your spreadsheet. There and using standard electrical calculations, you can get both the R and jX components of |Z|. Use Excell's plotting capabilities.
Very cumbersome, but it can be done.