The “Clean Energy for all Europeans” package highlights the need to create a resilient critical energy infrastructure in the European Union. Resilience is an emerging term to describe the energy system’s ability to withstand shocks caused by natural hazards, technical accidents, or intentional threats. In this paper, a framework to assess the resilience of energy systems using quantitative indicators is presented. Two main groups of resilience indicators are proposed that depend on what is being measured within the energy system: capacity (attribute-based) indicators or performance in the presence of disruption (performance-based) indicators. This study concentrates on the first resilience phase, when the energy system has to absorb the impact of the shock. The approach considers various disruptions (both internal and external) as triggering events. There is a particular focus on future shocks affecting the prospective energy system, which will have changed with respect to the current one. The future foresight capabilities and potential of the selected resilience indicators are demonstrated using calculations for the Lithuanian energy system. The results revealed that the most important factors that impact energy system resilience are a rich electricity production mix and the diversification of both supply and production in the prospective energy system.