How to Catch Latios and Latias without Master Ball

Here is the check list how to catch Latios and Latias:
1. AFTER YOU BEAT the game, the 4 Elites at the Victory Road, saved and back to your room, go down stairs, check out the TV news and you will now activate Latios OR Latias event, you will met it randomly on the map bushes. (Latios is in Ruby while Latias is in sapphire, Emerald you can choose either ONE ONLY.)
2. Bring bunch of pokeballs (great balls, ultraballs, net balls etc), some hyper potions and repels.
3. Get yourself a Level 30-35 Wobbuffet, trapinch, or any pokemon with 'mean look' move and high speed (Crobat or Golbat for example) to trap Latios or Latias in the battle.
4. Put Wobbuffet as first pokemon, spray repel and start walk in the bushes, if you're lucky you will met them in no time, you can try your luck at ROUTE 110, bushes in front of the entrance of the cycling road, or road 118 bushes near the berry master. Route 119/120 tall grass raining area, It really take some time and much luck, be patient.
5. lower health and cast them some status like PAR or FRZ will be more easy to catch, check out the video clip.

hope this help and happy hunting~