Construction (except for certain physical parameters such as size) and powering aren't the issue. The main point of a measurement mike is that its frequency response has been carefully measured at the factory, and is reliably traceable to a known reference standard. It should ideally be flat under the particular conditions (free-field or diffuse-field) in which it will be used--but to any extent that it's not, the deviations must be charted and made known explicitly to the end-user acoustician so that they can be taken into account while working with the mike.
As always, DSatz lays out excellent knowledge for us here. Thanks.
Earthworks makes a series of measurement mics which are designed/manufactured with consistent omnidirectional polar pattern in mind, among other things.
Their line of measurement mics includes some which extend a little beyond 20 kHz and some which go up to 50 kHz.
https://earthworksaudio.com/measurement/m50/As DSatz mentioned, the measurement mics will come with a calibration chart or a file. The details of these files are rather simple, and are the measurements of the exact serial numbered mic compared to a listed reference mic. I believe the contents of the file are literally the measurement at frequency, listed in the value in +/- dB. I'm attaching a sample image I found on the internet, from a place which calibrates mics.
You can purchase inexpensive measurement mics new and used, which lack calibration files. (usually cheaper than the same mic with the data)
In order to best utilize mics for frequency analysis, they should be calibrated, and the chart or file saved along with the mic, so it can be transferred to a future owner, or in case your computer crashes.
For advanced measurement applications, a series of matched mics may be needed. Meyer Audio in Berkeley has a set of matched calibration microphones which they use in their anechoic chamber where they measure each loudspeaker they build. Evidently, the higher number of mics you need factory-matched, the more costly it becomes. A set of 8 precision-matched mics costs a lot more than 4 pairs, from DPA.