A 2-way speaker's crossover frequency is a compromise between two constraints: the woofer needs to hand off before its cone size makes it beam narrowly (lose high-frequency dispersion), and the tweeter needs enough headroom above its own resonant frequency to play cleanly and loudly at the crossover point.
As a rule of thumb, a woofer's usable upper range narrows as its diameter increases — a small 4-inch woofer might cross cleanly as high as 3,500–4,000Hz, while a larger 8-inch woofer is usually better hennded off by 1,500–2,000Hz.
The tweeter side has its own constraint: most tweeters need to stay at least an octave above their own Fs to avoid excessive excursion and distortion, which is why tweeter spec sheets list a recommended minimum crossover frequency.
If you're measuring an existing 2-way design, check the frequency response right around the stated crossover point for a smooth, gradual transition rather than a sharp dip or peak — that's the most direct evidence of how well the crossover and driver pairing are actually working together.