The terms input impedance and output impedance are used quite often when it comes to amplifiers or when cascading circuits together to determine how each will load the other. While it all makes sense on paper, how can one measure the input and output impedances of a circuit also seeing that these are impedances and not resistances?
It's easy to get a rough idea by inserting a potentiometer in the wire. Dial down the resistance until you get a reading which is exactly half of the reading obtained prior to inserting the resistance. Measure the potentiometer value, and you have the circuit impedance.
This method may alter circuit operation. But an equal resistance makes things easy, rather than having to do calculations based on a very low ohm resistance.
In the general case, an impedance is comprised of a real (R) and a reactive (X) impedance part, forming a complex quantity. So what do you mean with "impedance not resistance"? Obviously a real impedance is easier to measure or to match than a complex one.
To narrow the problem range, you should mention the frequency of interest, e.g. audio or other low frequency application < 1 MHz versus RF > 10 MHz. Impedance matching concepts and measurement methods are quite different for it.
Exact method of the input impedance estimation may be taken from the small hf antenna tuning concept in portable transceivers (unbalanced bridge). As for the output impedance, load-pull techniques combined with maximum efficiency criterion seems right.