Machine translation provides powerful methods to convert text between languages, and is therefore a technology enabling a multilingual world. An important part of communication, however, takes place at the non-propositional level (e.g., politeness, formality, emotions), and it is far from clear whether current MT methods properly translate this information. This paper investigates the specific hypothesis that the non-propositional level of emotions is at least partially lost in MT. We carry out a number of experiments in a back-translation setup and establish that (1) emotions are indeed partially lost during translation; (2) this tendency can be reversed almost completely with a simple re-ranking approach informed by an emotion classifier, taking advantage of diversity in the n-best list; (3) the re-ranking approach can also be applied to change emotions, obtaining a model for emotion style transfer. An in-depth qualitative analysis reveals that there are recurring linguistic changes through which emotions are toned down or amplified, such as change of modality.