The acquisition and display of material artefacts is the raison d'être of museums. But what constitutes a museum artefact? Contemporary medicine (biomedicine) is increasingly producing artefacts that do not fit the traditional museological understanding of what constitutes a material, tangible artefact. Museums today are therefore caught in a paradox. On the one hand, medical science and technologies are having an increasing pervasive impact on the way contemporary life is lived and understood and is therefore a central part of the contemporary world. On the other hand, the objects involved in medical diagnostics and therapies are becoming increasingly invisible and intangible and therefore seem to have no role to play as artefacts in a museum context. Consequently, museums are at risk of becoming alienated from an increasingly important part of contemporary society. This essay elaborates the paradox by employing Gumbrecht's (2004) distinction between 'presence' and 'meaning'.