Concerns related to climate change and security of energy supply are pushing various countries to define strategic energy plans. Strategic energy planning for national energy systems involves investment decisions (selection and sizing) for energy conversion technologies over a time horizon of 20-50 years. This long time horizon requires uncertainty to be accounted for. Long-term planning for energy systems is often based on deterministic economic optimization and forecasts of fuel prices. When fuel price evolution is underestimated, the consequence is a low penetration of renewables and more efficient technologies in favor of fossil alternatives. This work aims at overcoming this issue by assessing the impact of uncertainty on strategic energy planning decisions. A classification of uncertainty in national energy systems decision-making is performed. A Global Sensitivity Analysis (GSA) is performed in order to highlight the influence of the model uncertain parameters onto the energy strategy. Optimization under uncertainty is then applied to a general Mixed-Integer Linear Programming (MILP) problem having as objective the total annual cost and assessing as well the IPCC Global Warming Potential LCIA indicator (CO2-equivalent emissions). The application focuses on the case study of Switzerland. It is shown that in the uncertain domain investing in more efficient and cleaner technologies can be economically optimal.