Measuring the pickup's resistance from one wire to the other is known as the "dc resistance" reading and it is usually 2k-12k, with most specimens lying at about 4k-6k in my experience.
As an impedance, this number only applies to a frequency of 0Hz.
To get an impedance for a musical frequency, say 1kHz, you must take the coil's inductance into account. Really, the capacitance needs to be considered as well, but the inductance dominates the calculations.
It used to be uncommon, but now many cheap DMMs have an inductance test. I have such a meter, and I have taken measurements of many pickups. They tend to measure from 1H-10H (H="Henries"). A coil in series is a natural low pass filter because coils can't pass high frequencies easily. The inductive reactance rises as frequency rises. Inductive reactance is the coil's special, frequency dependent, resistance. After calculating a reactance for a specific frequency, say 1kHz, you can add that to the dc resistance to get your rough idea of the pickup's impedance.
For an example pickup with 5k dc resistance and 5H inductance, the impedance at 1kHz is 36k. 1kHz is the fundamental tone about where the guitar neck ends (on the high "E" string). That's way more than what you would expect from your 5k dc resistance reading.
The 12th fret on the high "E" string, which has a fundamental of about 660Hz, has an only slightly better 20k impedance.
Stuff in the upper hearing range, ~10kHz is so loaded that "overwound" pickups aren't even able to generate the tones. A pickup winder going for a wide and even response must settle for lower henries.
Piezo pickups have the opposite problem of the wire wound magnetic pickups. The piezo can be thought of as a capacitor, and thus the piezo impedance is based on capacitive reactance.
A capacitor is a natural high pass filter. Piezo crystals do not transmit bass frequencies with ease. Whereas wound pickups lose treble easily, piezo pickups lose bass easily. The solution is basically the same for both: the piezo output must connect to a very high impedance that is sufficiently larger than the (large) impedance of the lowest frequency of interest (20Hz for extreme bass, 80Hz for a regular guitar low E, 40Hz for a bass guitar low E).