A new task ('CARER') was used to test claims of reduced empathy in autistic adults. CARER measures emotion identification (ability to identify another's affective state), affective empathy (degree to which another's affective state causes a matching state in the Empathiser) and affect sharing (degree to which the Empathiser's state matches the state they attribute to another). After controlling for alexithymia, autistic individuals showed intact affect sharing, emotion identification and affective empathy. Results suggested reduced retrospective socio-emotional processing, likely due to a failure to infer neurotypical mental states. Thus, autism may be associated with difficulties inferring another's affective state retrospectively, but not with sharing that state. Therefore, when appropriate measures are used, autistic individuals do not show a lack of empathy.