Catching pokemon in a pen and paper game

Related to this and this. If I am using tamed monsters as a magic system, there has to be a way to catch them. Or not? I am very confused about how to do it. On one hand I have the analogic ways:Getting into the wilderness (aka the tall grass) until a monster pops up, then catching them with a pokeball equivalent. This works perfectly on the games, but I see how it can become tedious on a tabletop. Grinding a place to find one pokemon that one player happens to want makes all the other players who dont have anything to do at that place just stop and watch the show. If I do it too easy so the pokemon is catched fast, its almost the same as giving the player the monster straight. An even more analogic version of this is if the monsters are not catch with pokeballs, but convinced to follow a leader by actually roleplaying and discovering the monster's motivations or personality. This is great to have sometimes, but having it as the main point of the game for sorcerers and not for the…