I believe #4 hardware cloth (1/4 inch) is what people use. I've also read that drones can have a hard time squeezing out of #4, and workers have trouble "dragging out the dead" sometimes. There shouldn't be many drones left by the time you're putting mouse guards on though.
Anyone with experience using this kind of mouse guard? Any other home-made mouse guard ideas? I bought Maxant stainless-steel guards for my first hives. They're very spiffy, but I'd like to find a more economical option (and I love things homemade).