I've had two rejected submissions come in because I didn't have any means of recording them. I don't have a capture card, do you have any suggestions?

(Yes, I know you can just point it at the TV, but I'm playing handheld games)

Handheld is broad - if it’s something like a gameboy game, you could use the GBP on GameCube it a Super Gameboy 2 on SNES with a capture card to record the video. If it’s a DS, your options are limited without purchasing a DS cap card and having it installed. You can point a camera at it if you get creative with mounting a webcam or on top of a box and point it down at your hands.

Depending on the game, emulator might be an option, so check with the mods and rules of any game in question.