© 2015 The Authors. Policy goals to transition national energy systems to meet decarbonisation and security goals must contend with multiple overlapping uncertainties. These uncertainties are pervasive through the complex nature of the system, the long term consequences of decisions, and in the models and analytical approaches used. These greatly increase the challenges of informing robust decision making. Energy system studies have tended not to address uncertainty in a systematic manner, relying on simple scenario or sensitivity analysis. This paper utilises an innovative UK energy system model, ESME, which characterises multiple uncertainties via probability distributions and propagates these uncertainties to explore trade-offs in cost effective energy transition scenarios. A linked global sensitivity analysis is used to explore the uncertainties that have most impact on the transition. The analysis highlights the strong impact of uncertainty on delivering the required emission reductions, and the need for an appropriate carbon price. Biomass availability, gas prices and nuclear capital costs emerge as critical uncertainties in delivering emission reductions. Further developing this approach for policy requires an iterative process to ensure a complete understanding and representation of different uncertainties in meeting mitigation policy objectives.