How to catch latias and latios without cheats?

If you "Pick Red" after you defeat the Elite Four, Latias will be roaming the Hoenn Region. If you "Pick Blue" after you defeat the Elite Four, Latios will be roaming the Hoenn Region. However, you can only pick one.

You can obtain the other one by trade.

Hope this helps!

No, it doesnt help. Saying that it will randomly appear is not helpful it is obvious.

Well at one point when you defeat the elite four your mom will say somthing about the tv bla...bla...bla...then she will ask you the color of the Pokemon you saw red or blue so you can only get one unless you get another Pokemon emerald and beat the elite four and trade the other

As soon as you beat the leuge just go to be there on the TV and it will ask for which color it was but for the other you Need a special ss ticket

You guys are stupid he/she are asking how to catch them. Well they are roaming so they will change location every time you go to another area whether it be by flying or walking. You can see this on your pokedex if you've already seen the Pokemon before by going to area on it. You want to go to a route right where it changes and go back out and into the route and check your pokedex for the area every time you do so. Once you are in the same route as he or she is( the area is highlighted in your pokedex for latios/latias) then look around in the tall grass, water, etc. And you should find him soon. A better way of looking for him when he's in the area is to get a Pokemon that is level 30-40 as your first slot Pokemon ,and make sure your in a low-level area, then use a repellent and search the grass. The repellent works for Pokemon under your first slot pokemon's level, and Latios/Latias is a level 40. Should help!
This is also a legendaries guide for Emerald: http://www.gamefaqs.com/gba/921905-Pokemon-emerald-version/faqs/63192#section67

First you should put a Pokemon that is LVL 40 or lower in your first slot
Then get the acro bike
You to route 110 and use a repellant
Go to the grass and jump for about 30 secs
If latias/latios does not appear go into the bike house near it
Then repeat the steps
That's how I found latias =)
Hope this helps

Best course of action: have a fairly high level trapinch (lvl 30-40) with the ability ARENA TRAP. That way the latias/latios wont flee from you. Then just try ultra balls, timer balls. I used up all my pokeballs and caught latios with luxury ball.