In the wake of the outbreak of the COVID-19 crisis, the Swedish and Swiss governments adopted a similar policy approach. They enacted mostly non-binding measures to contain the epidemic, relying on the high level of interpersonal trust and trust in political institutions that exist in both of these (broadly comparable) countries to ensure compliance. However, unlike Sweden’s strategy, the Swiss policy response evolved during the early weeks of the “first wave”, achieving public health and socioeconomic results that have been considered as satisfactory, notwithstanding the complex institutional setting and policy process, the central location of Switzerland in continental Europe, its openness and its closeness with deeply affected regions in Italy and France. To shed light on this policy response and to draw lessons from it, this paper firstly discusses the role played by the new Swiss Epidemics Act. This law centralises decision-making capacity at the federal level and expands the competences of the central government, while leaving leeway to subnational units for implementation and recognising the need for increased international regulatory cooperation. Secondly, it shows how such a solution – a multi-level arrangement steered from the federal level with quite strong vertical and horizontal coordination mechanisms – could work as a blueprint for a European Health Union.