A simulation-based framework for multifidelity uncertainty quantification is presented, which informs and guides the design process of complex, large-scale, multidisciplinary systems throughout their life cycle. In this framework, uncertainty in system models is identified, characterized, and propagated in an integrated manner through the analysis cycles needed to quantify the effects of uncertainty on the quantities of interest. This is part of the process to design systems and verify their compliance to performance requirements. Uncertainty quantification is performed through mean and variance estimators as well as global sensitivity analyses. These computational analyses are made tractable by the use of multifidelity methods, which leverage a variety of low-fidelity models to obtain speed-ups, while keeping the main high-fidelity model in the loop to guarantee convergence to the correct result. This framework was applied to the James Webb Space Telescope observatory integrated model used to calculate the wavefront error caused by thermal distortions. The framework proved to reduce the time required to perform global sensitivity analyses from more than 2 months to less than 2 days, while reducing the error in the final estimates of the quantities of interest, including model uncertainty factors. These technical performance improvements are crucial to the optimization of project resources such as schedule and budget and ultimately mission success.