How to measure the nozzle diameter?

The correct tool for measuring a hole usually is a Bore Gauge, but that doesn't work for super small holes like nozzles and generally needs holes at least 5 mm in diameter. For those small holes, there's a different tool:

These are Thread Measuring Wires of known diameter. While generally used to find out the depth of thread you are dealing with in a threaded (or if your thread is correct depth), they are also useful for measuring small bores. In this capacity, You'll use them as follows: The diameter of a hole can accompany any smaller diameter, but never a larger diameter wire, so a clean nozzle of 0.4 mm should accompany a 0.3 and o.35 easy but not a 0.45. A 0.4 might or might not fit, depending on how accurate the hole is. You'll need a very fine set of thread gauges though, and wires, pins, and needles of known diameter are a suitable replacement for this.

I have found that normal measuring devices are not particularly helpful with accurately measuring nozzle diameters. But you're already off to a great start.

What is helpful is to take them somewhere that has a wide assortment of drill bits, and find which two adjacent sizes will and will not fit in the (clean) nozzle; then convert the diameters to mm (if needed), and your nozzle is larger than the small bit, but smaller than the large bit. From that, you should be able to narrow it down to a standard dimension.