National infrastructure (NI) systems (i.e., energy, transport, water, waste, and information and communications technology) provide essential services to the economy and contribute to human well-being. These systems have evolved over centuries, being planned and implemented piecewise, and are mostly managed in isolation from one another. Here, we argue that the growing interconnection between these systems and the convergent challenges ahead (i.e., demographic, technological, and climate change) call for an integrated “system-of-systems” approach to managing NI. Toward that end, we propose a modelling framework for the long-term (to 2100) simulation of NI system performance in a highly uncertain future. The approach is based on the assessment of the performance of infrastructure services in a wide range of possible future conditions. This robust optimization is used to identify cross-sectoral strategies that ensure satisfactory infrastructure performance. We demonstrate the framework using Great Britain’s NI as an example.