Terra and Marine Caves
These two caves are where you can find Groudon at Terra Cave, and Kyogre at Marine Cave. The caves can appear in four different spots each after defeating the Elite Four and becoming Pokémon Champion.
Terra Cave and Groudon
Terra Cave can be found either on Route 105, 125, 127, or 129. In order to check which route it's on, talk to the scientist on the second floor of The Weather Center. The location can change if you're not fast enough finding it.
Once you find it, proceed through it until you find Groudon. He's at level 70.
Marine Cave and Kyogre
Marine Cave can be found either on Route 105, 125, 127, or 129. In order to check which route it's on, talk to the scientist on the second floor of The Weather Center. The location can change if you're not fast enough finding it. You'll need a Pokémon that knows Dive in order to reach the cave.
Once you find it, proceed through it until you find Kyogre. He's at level 70.
Best of luck capturing them both.
Source:
1 Serebii, Webmaster. "Pokémon Emerald - Terra Cave" Serebii.net. Revision Date Unknown. 06 Jan 2009 http://www.serebii.net/emerald/shorecave.shtmll.
2 Serebii, Webmaster. "Pokémon Emerald - Marine Cave" Serebii.net. Revision Date Unknown. 06 Jan 2009 http://www.serebii.net/emerald/seacave.shtml.
