No, they stay at the same level. However in some games they gain an one-off 15-16 level increase after you've completed the rest of the game.
Chat with our AI personalities
Unfortunately the only area for good training is the Pokemon league.
You should swap your party Pokemon with a friend and get them to level them up so it gets double the exp point. Also you could give it an exp share and take it to the Pokemon league, if it is too weak to fight then it doesnt have too but it still gets alot of EXP the average Pokemon will grow to level 32 if you take it through the Pokemon league with an EXP Share (I take it through with a level 100 Rayquaza so this may vary for other Pokemon).
the easiest way to level up your Pokemon to put it in daycare Pokemon will level up soon.Trade the Pokemon to friend and have it hold a lucky egg it will level up quickly.
Train your pokemon.
level 100