Third-party punishment (TPP), in which unaffected observers punish selfishness, promotes cooperation by deterring defection. But why should individuals choose to bear the costs of punishing? We present a game theoretic model of TPP as a costly signal of trustworthiness. Our model is based on individual differences in the costs and/or benefits of being trustworthy. We argue that individuals for whom trustworthiness is payoff-maximizing will find TPP to be less net costly (for example, because mechanisms that incentivize some individuals to be trustworthy also create benefits for deterring selfishness via TPP). We show that because of this relationship, it can be advantageous for individuals to punish selfishness in order to signal that they are not selfish themselves. We then empirically validate our model using economic game experiments. We show that TPP is indeed a signal of trustworthiness: third-party punishers are trusted more, and actually behave in a more trustworthy way, than non-punishers. Furthermore, as predicted by our model, introducing a more informative signal--the opportunity to help directly--attenuates these signalling effects. When potential punishers have the chance to help, they are less likely to punish, and punishment is perceived as, and actually is, a weaker signal of trustworthiness. Costly helping, in contrast, is a strong and highly used signal even when TPP is also possible. Together, our model and experiments provide a formal reputational account of TPP, and demonstrate how the costs of punishing may be recouped by the long-run benefits of signalling one's trustworthiness.