I don't think you can catch either of them until AFTER you've beaten the elite four and
become the Pokemon master. But once you've done that, go to the Weather Institute (not
far from Fortree City). Then talk to the people inside until one of them mentions strange
weather on "Route ____". Remember whereabouts they mention and go straight where they're
talking about. You should notice that it'll either be like a heat-wave or thundery rain.
This will determine which of the 2 Pokemon you'll have the opportunity to catch. There
should be a hidden cave entrance somewhere nearby. Eventually it'll take you to the
Pokemon you're looking for. PS. I'm not sure whether or not you can catch BOTH of them
and whether or not you have to use the "Master Ball" to capture the Pokemon. Hopefully
I've been of some help though. =o)

I forgot to sign in before I posted that message! Lol. Silly me. =o)

I've just checked an online source and you CAN catch both Groudon and Kyogre. I thought
Emerald was the same as Ruby/Sapphire, because you could only get one or the other. But
you can DEFINITELY get both Pokemon in Emerald. =o)

though i couldnt find them in my emerald and i beat the elite four.i did go to weather
institute but when i talk to the guy and go to the route i cant find the cave,why?