Inconsistencies in science take several forms. Some occur at the level of substantive claims about the world. Others occur at the level of methodology, and take the form of dilemmas, or cases of conflicting epistemic or cognitive values. In this article, I discuss how methodological dilemmas arise. I then consider how scientists resolve them. There are strong grounds for thinking that emotional judgement plays an important role in resolving methodological dilemmas. Lastly, I discuss whether and under what conditions this reliance on emotional judgement is rationally warranted. I consider two possible mechanisms, based on coherence and induction, able to ensure that scientists’ emotional responses to methodological dilemmas are rationally warranted.