Here's a trick:
The females are usually green. The males are usually smaller, skinnier and browner. Catch yourself one of each and then put them between the screen and the window. Then put katydids and grasshoppers in there with them and watch the show. Eventually the male and female hook-up. The male climbs up and stays on for up to 3 days. Finally, the female reaches around and takes off the male's head.
Shortly thereafter, the female exudes a sticky mass-- looks like foam insulation that sticks to the screen. She then goes off her feed and dies. Leave the mass on the screen and wait.
In the spring, after it warms up a little, the mass will suddenly erupts and hundreds of little preying manti will suddenly fill up the screen. Open up the screen a crack and let them out.
Wash, rinse repeat.