He was referring to Pok�mon Sapphire, so I gave him a relevant answer. In Pok�mon Emerald, however, dark_blaziken is correct; use the Match Call option to arrange a battle with Trainers who want a rematch.
To avoid any confusion, I'm moving this to Pok�mon Sapphire.
If you see me posting, it's because I've been asked to. Which I guess would mean I'm taking requests.