In this paper we study the use of confidence measures for an on-line handwriting recognizer. We investigate various confidence measures and their integration in an isolated word recognition system as well as in a sentence recognition system. In isolated word recognition tasks, the rejection mechanism is designed in order to reject the outputs of the recognizer that are possibly wrong, which is the case for badly written words, out-of-vocabulary words or general drawing. In sentence recognition tasks, the rejection mechanism allows rejecting parts of the decoded sentence.