The worst way to settle a tie in sports: devise some ridiculous theatrical spectacle which has only a small bit to do with the actual game. (For example: a soccer shoot out.)
The best way: create the purest and clearest form of competition in the sport. (For example: two women who tied in the 100m, racing again, alone, on the track.)
Nick Thompson asks, “Will track show soccer how to break a tie?” http://nyr.kr/MjRYwV
Naturally, Track is both superior and fundamental to all other athletics.