Just caught Mew using the teleport from Gandalf(Abra)!
Wut
There is a trainer around a corner too the left past the 5 trainers on the bridge in the 3rd town and as soon as you move into the aggro range of him hit pause and use teleport(save game before aggroing him, after that there is another trainer that is on the way to Bills house>>

, fight him at least one space away from where he is so he has to move to you(this keeps the game from freezing), defeat his slowwhatever and use teleport again, go back to the bridge again and the pause menu will automatically activate, open the pokemon window then close out of it and hit exit, the mew fight will begin as soon as you do.
I used a Lv8 sandshrew named Shukaku and spammed scratch since it does little damage, brought lots of potions/pokeballs to
Teleport from Abra or the flying w/e from Fearow also works
This also works in Blue version apparently since this is what I got the info for and decided to try it on Yellow anyways...