Uncertainty is a fact of project life. Most decisions that are made on a safety-critical project involve uncertainty, the consequences of which may be highly significant to the safe and timely delivery of the project. Based on interviews with project management practitioners on nine large-scale civil nuclear and aerospace projects, we explore how uncertainty emerges, and how project management practitioners identify, analyse and act on it. We make three important contributions. First, we present three approaches – structural, behavioural and relational – that individuals and organizations can adopt when contending with project uncertainty. Secondly, we characterize nine dualities at play in the management of project uncertainty and thirdly, we identify key differences between how civil nuclear and aerospace project managers confront project uncertainty, which have important implications for how projects might be organized in both these industry sectors. Drawing attention to the structural, behavioural and relational approaches to project uncertainty and the tensions that manifest themselves in each approach should enable the project management community to make progress in environments of high uncertainty where situations are often complex, rapidly changing and confusing, and yet where, for reasons of safety, failure is not an option.