The aim of the article is to reframe speculation from being seen as synonymous with unacademic conjecture, or as a means for questioning consensus and established narratives, to becoming a productive practical engagement with the archaeological and responding to its intrinsic uncertainties. In the first part of the article, we offer a review of speculation in the history of archaeological reasoning. In the second part, we proceed to discussing ways of embracing the speculative mandate, referring back to our engagements with the art/archaeology project Ineligible and reflections on how to work with the unknowns and uncertainties of archaeology. In the third and last part, we conclude by making the case for fertilizing the archaeological potential nested in the empirical encounter, creating more inceptions than conclusions, fostering ambiguities, contradictions and new spaces of experiential inquiry. This leads us to suggest that—when working with the archaeological—speculation should be seen not only as a privilege, but also as an obligation, due to the inherent and inescapable uncertainties of the discipline. In other words, archaeology has been given a mandate for speculation through its material engagements.