How to measure microphone output impedance?

I assume one measures the output impedance of a microphone by assuming the mic is a perfect AC voltage source in series with an unknown value resister.  The goal is to measure that resister.  The simplest way I can think of is to place a variable resister in series with the mic and adjust it until the voltage is exactly half of what is was.  The impedance is whatever the resister is set to.

Now assuming the above is how it's done.  I'd would need a source of sound for the mic and of course phantom power if the mic needs that.  What is are people using for a sound source and is there a "standard" audio frequency for measuring impedance?

Same question about measuring frequency response.  Making noise from 20Hz to 20KH is not easy if you need to control the volume to (say) 0.1db.  Should I try using an un controlled source like a home HiFi speaker connected to an signal generator and then pair my microphone under test with a calibrated mic?  Again what are people here using?

The best way to measure output impendance is to apply AC signal at the output of the microphone.
Of course, you should make it AC coupled.
Also, signal level is important: at very high level microphone's output will saturate and give wrong result.
I have nice russian generator that has 600 Ohm output impendance and output voltage up to 10V~. When I need to measure output impendance, I apply signal through big electrolytic capacitor.
I can choose any frequency from 5Hz to 500kHz.
Hope it helps.

I would do it like this:
Put the microphone in front of a loudspeaker with a steady tone on it. (400 Hz or 1 KHz.)
Measure the unterminated output of the microphone with an AC millivoltmeter*.
Then connect a 1000 ohms potentiometer to the output of the microphone and adjust it until the output drops 6 dB compared to the 'unterminated' output level.
In this case the resistance of the potentiometer will be the same as the output impedance of the microphone.
(That is: at the frequency you measured. Dynamic microphones will have a frequency dependent output.)

*: you may have to use a transformer to get rid of the phantom voltage and to convert the balanced microphone signal to an unbalanced signal for the AC millivolt meter. Take care that the impedance of the transformer is high compared to the impedance of the microphone.