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Many of our most important goals require months or even years of effort to achieve, and some never get achieved at all. As social psychologists have lately emphasized, success in pursuing such goals requires the capacity for perseverance, or "grit." Philosophers have had little to say about grit, however, insofar as it differs from more familiar notions of willpower or continence. Jennifer Morton and I propose that grit has an important epistemic component, in that failures of perseverance are often caused by a significant loss of confidence that one will succeed if one continues to try. Correspondingly, successful exercises of grit often involve a kind of epistemic resilience in the face of failure, injury, rejection, and other setbacks that constitute genuine evidence that success is not forthcoming. Given this, we discuss whether and to what extent displays of grit can be epistemically as well as practically rational. We conclude that they can be (although many are not), and that the rationality of grit will depend partly on features of the context the agent normally finds herself in.