This paper investigates ethical and sociotechnical dilemmas surrounding the implementation of biometrics such as facial recognition and digital fingerprints at a large Swedish airport, part of the EU’s Entry/Exit System (EES). We describe the EES as a supranational infrastructure aimed at enhancing border security across national and European levels. Drawing on empirical fieldwork from site visits, interviews, and document analysis, we explore the tensions inherent in this development. While biometrics are framed as solutions to strengthen security and efficiency, they also raise serious concerns about democratic values and rights. We draw on the concept of approximation to show how these technologies operate not by confirming fixed identities, but by inferring degrees of similarity to predefined risk profiles. This epistemic logic, based on probabilistic reasoning, introduces new forms of judgement at the border that may obscure legal standards, reinforce bias, and shift the locus of authority from humans to opaque algorithmic systems. The paper identifies several dilemmas and highlights how biometric systems risk normalising surveillance within everyday border control. We position the airport as a techno-political space shaped by public–private partnerships and algorithmic infrastructures, and call for critical scrutiny of the epistemic assumptions and power asymmetries these systems reproduce. As biometric borders continue to evolve, there is a pressing need for an ongoing, critical interrogation of the normative assumptions, power asymmetries, and epistemic practices embedded in algorithmic border control. Without such reflection, we risk entrenching surveillance systems that not only monitor movement but fundamentally reshape how personhood, risk, and legitimacy are understood at the border. If borders are no longer about who you are, but about who the system believes you might be, what does that mean for the future of rights, accountability, and democratic oversight?