In the Ultimatum Game (UG), incurring a cost to punish inequity is commonly termed altruistic punishment. This behaviour is thought to benefit others if the defector becomes more equitable in future interactions. However, clear connections between punishment in the UG and altruistic behaviours outside the laboratory are lacking. We tested the altruistic punishment hypothesis in a sample of extraordinarily altruistic adults, predicting that if punishing inequity is predictive of altruism more broadly, extraordinary altruists should punish more frequently. Results showed that punishment was not more prevalent in extraordinary altruists than controls. However, a self-reported altruism measure previously linked to peer evaluations but not behaviour, and on which extraordinary altruists and controls did not differ, did predict punishment. These findings support suggestions that altruistic punishment in the UG is better termed costly punishment and may be motivated by social, but not necessarily prosocial, concerns. Results also support prior suggestions that self-reported altruism may not reliably predict altruistic behaviour.