As both @Rory M and @Alexander Galkin suggest, there are various non-visual mating behaviors to allow these species to select mates and also allow taxonomists and researchers to identify these species. And they hit on the two major ones, courtship rituals (mating calls, throat bulging, dancing) and pheromones.
Let's have a look at some two examples:
- The widespread amazonian frog Allobates femoralis is now being approached as a species complex, with mating differences between the biologically distinct species varying from mating call note differences to cephalic amplexus (head grabbing during mate selection) and other various behavioral differences.
- Some crickets mate preferentially based on their species-specific song. Though, there is probably some genetic mixing with those crickets.
I think it's important to note that the species are cryptic because we as humans have decided they're hard to tell apart. Now, that similar morphology is also potentially difficult for predators to tell apart, or may be used by one or both species to parasitize on the other, it may be kept similar by sexual selection, or it may just not have great selective pressures to change. But the important part is that "cryptic species" is a box that we've created to describe traits we see.
Cryptic species as a window on diversity and conservation is a decent overview paper. (it's avaliable here if you don't have journal access)