Ruby & Sapphire Roaming Hoenn
Once you become Champion, one of the eon twins takes to the skies and drifts across Hoenn: Latios in Ruby, Latias in Sapphire. Pinning the wanderer down is a hunt all its own.
Roaming Hoenn is in Hoenn. In the story it comes after S.S. Tidal and before Southern Island.
ROAMING HOENN MAP
Pokemon Encounters
One of the eon twins roams Hoenn after the Hall of Fame: Latios in Ruby, Latias in Sapphire, both circling the region at level 40. They flee the instant a battle starts, so a Pokemon that knows Mean Look or a reliable sleep move makes the catch far easier.
Latias
Roaming Hoenn Guide
Latios roams Hoenn in Ruby and Latias roams in Sapphire, both at level 40 once you're Champion. They flee the moment battle starts, so lead with a fast Pokemon that knows Mean Look to trap them, then whittle their HP down before you start throwing balls.
It's deliberate in Ruby and Sapphire. The roamer is Latios in Ruby and Latias in Sapphire, while the Eon Ticket event on Southern Island gives you the other one. So a single save can end up with both Eon Pokemon, just from two different sources.