Inserting a large value resistor in series with a signal generator (1000 Ohms in Ernie's example) you are essentially converting the the generator to a constant current source because the magnitude of the speaker's impedance is much lower than the resister's value. This scheme is not absolutely accurate, but it will be within a few percent and this is good enough for practical purposes. You can use a 10K resistor, but the voltage readings will be much lower. It is trivial to convert the meter reading into the magnitude of the impedance.

If you want valid results for a wide frequency range, pay attention the frequency response of the AC voltmeter. Many are designed for reasonable accuracy at 50, 60, or 400Hz and accuracy at other frequencies is not specified. You can quickly check your setup by assuming that the power amplifier in Ernie's example is flat, then measure the output voltage of the power amplifier at various frequencies. If the voltage indication varies significantly, suspect the generator or the voltmeter. If the generator is reasonable quality, then the voltmeter is not appropriate for the task.

You can use this same scheme to check a network of in-wall volume controls. This is a very handy technique to quickly check the complete system. You can determine if the system configuration is reasonable by inserting the resistor and making a quick impedance sweep. Mercifully, there will not be grossly loud strange noises to frighten inhabitants of the venue.

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I've seen a few cheap VOM's or dedicated devices that claim to be able to measure speaker impedance. Unfortunately, the designer has no grasp of the purpose of his device because it measures the magnitude of the impedance at a single frequency, usually 1kHz. This is not a very interesting frequency for our purposes.