Bass writes: Rematch is a tie breaker used in some of the more important go tournaments.

which important tournament? we should state which ones (a couple would be fine, preferably the most important) with the year , if not the full date, of the tournament.

In major Japanese titles like the Meijin and Honinbo, the challenger is decided in a round-robin league. In case of a tie, a play-off between the tied players is played to decide the challenger.