Reliance on point estimates when developing hybrid energy systems can over/underestimate system performance. Analyzing the sensitivity and uncertainty of large-scale hybrid systems can be a challenging task due to the large number of design parameters to be explored. In this work, a comprehensive and efficient sensitivity/uncertainty methodology is applied on two fuel cell hybrid systems to help analysts to investigate hybrid systems more efficiently. This methodology also includes a step-by-step approach to perform design optimization under uncertainty of energy systems. The two hybrid systems are: molten carbonate fuel cell with thermoelectric generator (MCFC-TEG) and phosphoric acid fuel cell with refrigerator (PAFC-REF). Various sensitivity and uncertainty methods are utilized to analyze the design parameters and their effect on the performance of these two systems. These methods perform local and regression-based sensitivity analysis, Monte Carlo uncertainty propagation, parameter screening, and variance decomposition. Detailed approach is adopted to identify and rank the influential design parameters for each system. Results demonstrate that the optimum power output of the MCFC-TEG has 10% uncertainty, driven mainly by the operating temperature, cahtode activation energy, TEG figure of merit, and TEG thermal conductivity. However, PAFC-REF is more reliable with larger power output and 1.4% uncertainty, driven by the charge transfer coefficient, heat transfer in the refrigeration cycle, cold reservoir temperature, and operating temperature. Based on this identification, design optimization under uncertainty is performed using these sensitive parameters to improve the system performance through increasing the power output and reducing its uncertainty. Published by Elsevier Ltd on behalf of Hydrogen Energy Publications LLC.