Depends on how much time you have to spend on monitoring their breeding sessions. Monitoring means that you have to give your utmost attention. If your smartphone distracts you and in that split second, something could go terribly wrong.
In the past, I always placed the male a couple inches behind the female, and then we play the waiting game. I would watch as the male's eyes and antennae lock on to the female, and then he would slowly walk towards her. Ever so slowly, one step at a time, one cautious step at time. Then he makes the final jump onto her back, and holds on for dear life.
Tonight, however, I saw this thread, and plus, I don't have time tonight to sit for hours and watch the shy male orchids walk ever so slowly towards the female. I just took the male out of the container, put him on the tip of my finger, and moved the mantis so his face is close to the female's wings. His antennae would bend forwards, as if to examine the female. That is a good sign, meaning he is interested in mating. Then, I give a little blow of air, and the male walks on to her back and clutches on tightly. You can see he is in mating position since his body is flattened and he will start drumming in order to get the female to cooperate and bring her abdomen to one side so he can connect. This helped get my 2 pairs connected. So happy
There is a caveat. If you simply grab a male and drop him on the female, he may not even be in "the mood" and would walk right over the female as if she's a piece of furniture or inanimate plant.This is extremely dangerous because some of these "clueless" males walk straight into the female's raptorials.
If you have clueless males, your best bet would be to wait a week or two. Maybe the males are not ready or even the females are not ready.