1)
Make the contests in game as close to the anime contests as possible. Two rounds. One where you can select moves. Maybe one move, and then a combination of directional buttons. Maybe two moves to work in tandem, though some moves would only work well with certain others (i.e. you probably shouldn't use razor leaf with flamethrower). Depending on how well this is executed, you get ranked and move onto the next round.
Same shtic, though with pokemon battles of course. Now, you could try to go straight up battle stlye and just win via KO. However, you only have so many turns (since a time limit on a turn based game would be dumb) to do so, so having more points is the preferable method of victory. You may pick moves in tandem, and still issue commands for different effects (i.e. the directional buttons) for winning you more points, or causing your opponent to lose more.
2)
Actual rewards. Make the flashier TMs, or perhaps contest equivalent items winnable the same way you buy things with battle points. TMs like maybe Attract, the weather moves, or other such attacks would be obtained here.
3)
Hell, while we're at it, make the contests an entire optional side quest/story. Wasn't there some guy in DPP who was trying to be a league trainer and a coordinator? Give us different contests with different towns, each with different sets of rules. Like, only water types, or only Cool moves. Something like that. Essentially have it so if the player so chooses to go through the whole contest run, they'll be at the big finale competition around the same time they'd hit the pokemon league. In fact, one step further. Make the final competition take place AT the league.
