One way to "measure" the impedance is to use an audio oscillator connected to a small speaker, an oscilloscope or VTVM (must be a high-impedance voltmeter, not a VOM), and a variable resistor like two terminals of a potentiometer.
Connect the output of the microphone element to the scope or VTVM to measure its "open circuit" output voltage. Set the audio oscillator to 1 kHz, and adjust its output to a reasonable (equivalent to voice volume) level. Place the microphone element next to the speaker, so the oscillator is modulating the system. Look at the scope or VTVM and sweep the audio oscillator down to 300 Hz and up to 3000 Hz while watching the element output level. You're now looking at the frequency response of two transducers: The speaker and the microphone. It doesn't matter. Tune the oscillator to a frequency that represents about the "average" mic element output: For example, if sweeping from 300 to 3000 Hz, the output as measured by the scope or VTVM varies between 200mV and 400mV, try to pick a frequency where the output is 300mV, or about midway between the two extremes.
Don't adjust the oscillator output level or change frequency any more. Also, don't move the mic element or the speaker. Record the voltage measured. Let's say it's 300mV.
Now, connect a 1k Ohm potentiometer directly across the mic element and the scope or VTVM. Adjust it about mid-way, so it's set around 500 Ohms. Record the voltage. If the pot is set to 500 Ohms and the voltage drops in half, say to 150mV, then the microphone's impedance is 500 Ohms. Whatever load resistance creates a 50% drop in open-circuit output voltage is the approximate impedance of the microphone.
For high-impedance mikes, you'd need a much larger resistor (pot), possibly 50k or even 100k Ohms.
This is a very simple test that only takes a minute to perform, but obviously requires some equipment that many hams won't have. But it's about the easiest way I know of to determine a transducer's impedance, and the equipment involved is not exotic or expensive. In lieu of an audio oscillator, you could use your own ham SSB/CW receiver, tuned to a steady carrier signal such as a crystal calibrator, and that receiver's speaker, with the "test mike" resting close to the speaker. Then, the only "test equipment" you'd need is a scope or VTVM.
To use a high-impedance mike with a low-impedance (mike input) transmitter, a matching transformer might work; however, you'll lose a lot of signal this way. The transformer, while matching the impedance, will also be stepping down the output voltage of the microphone...and might step it down so low that it won't work with your transmitter. It's always worth a try! See what happens. A better way is to use a studio-type microphone preamp or mixer, one with a high-Z input and low-Z output. That will perform the matching function, but with active circuitry, provide you with a higher and adjustable output level.
73 de Steve WB2WIK/6