Master Ball which you can get at the (Team Magma or Team Aqua) hideout
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How do you catch latios in Pokemon sapphire
If you have already beaten the elite four and have Latios or Latias already roming around in emerald then you can chase it down till you are in the same vicinity as it and go into the grass to see it appear. toss a master ball at it and you will have the latios or latias. Of course it's best that you clone the master ball first so that you can catch the other one the same way.
In Pokemon ruby you can catch latios but not latias, in Pokemon sapphire you can catch latias not latios, in emerald you can choose. Use your master balls on them so they wont fly away. You can use other types of balls, eg timer ball, ultra ball, or great ball on the other legendaries.
get a yoshi!
The same way you would catch a normal Pokemon. The only difference is is that the Pokemon is shiny.