Discussions of the development and governance of data-driven systems have, of late, come to revolve around questions of trust and trustworthiness. However, the connections between them remain relatively understudied and, more importantly, the conditions under which the latter quality of trustworthiness might reliably lead to the placing of ‘well-directed’ trust. In this paper, we argue that this challenge for the creation of ‘rich’ trustworthiness, which we term the Trustworthiness Recognition Problem, can usefully be approached as a problem of effective signalling, and suggest that its resolution can be informed by a multidisciplinary approach that relies on insights from economics and behavioural ecology. We suggest, overall, that the domain specificity inherent to the signalling theory paradigm offers an effective solution to the TRP, which we believe will be foundational to whether and how rapidly improving technologies are integrated in the healthcare space. We suggest that solving the TRP will not be possible without taking an interdisciplinary approach and suggest further avenues of inquiry that we believe will be fruitful.