In 1987, Roy Sorensen coined the term ‘parahistory’ to denote the study of genuinely anachronistic artefacts delivered by time travel.1 ‘Parahistory’ would thus stand to history rather as parapsychology is claimed to stand to psychology, i.e. the parahistorian would study historical data that were obtained through channels that orthodox science does not recognise. How might one establish credentials as a time traveller? What sort of evidence could a time-traveller point to in support of claims that would presumably command a great deal of scepticism? While successful predictions might be one confirmatory tool, supporting evidence needn't take the form of predictions. (Although Sorensen offers an intriguing argument that a Humean about miracle-testimony would be obliged to reject any testimony to the occurrence of time travel.) Perhaps artefacts that time travellers retrieve from other times (past or future) could usefully supplement testimonial or predictive evidence for the parahistorian. However, this paper will argue, any appeal to past-artefactual evidence for parahistorical claims faces a dilemma that threatens to undermine its value: appeals to past-artefact evidence must either collapse into appeals to predictive evidence or see their value diminished by such past artefacts' necessarily exhibiting contradictory indicators of age and period.