This paper presents sensitivity and resilience analyses for a trigeneration system designed for a hospital. The following information is utilized to formulate an integer linear programming model: (1) energy service demands of the hospital, (2) technical and economical characteristics of the potential technologies for installation, (3) prices of the available utilities interchanged, and (4) financial parameters of the project. The solution of the model, minimizing the annual total cost, provides the optimal configuration of the system (technologies installed and number of pieces of equipment) and the optimal operation mode (operational load of equipment, interchange of utilities with the environment, convenience of wasting cogenerated heat, etc.) at each temporal interval defining the demand. The broad range of technical, economic, and institutional uncertainties throughout the life cycle of energy supply systems for buildings makes it necessary to delve more deeply into the fundamental properties of resilient systems: feasibility, flexibility and robustness. The resilience of the obtained solution is tested by varying, within reasonable limits, selected parameters: energy demand, amortization and maintenance factor, natural gas price, self-consumption of electricity, and time-of-delivery feed-in tariffs.