The primary objective of this work was to develop and demonstrate a process for accurate and efficient uncertainty quantification and certification prediction of low-boom, supersonic, transport aircraft. High-fidelity computational-fluid-dynamics models of multiple low-boom configurations were investigated, including the Lockheed Martin SEEB-ALR body of revolution, the NASA 69 deg delta wing, and the Lockheed Martin 1021-01 configuration. A nonintrusive polynomial chaos surrogate approach was used for reduced computational cost of propagating mixed inherent (aleatory) and epistemic uncertainty through both the computational-fluid-dynamics model and the near-field to ground-level boom propagation model. A methodology has also been introduced to quantify the plausibility of a design to pass a certification under uncertainty. Results of this study include the analysis of each of the three configurations of interest under inviscid and fully turbulent flow assumptions. A comparison of the uncertainty outputs and sensitivity analyses between the configurations is also given. The results of this study illustrate the flexibility and robustness of the developed framework as a tool for uncertainty quantification and certification prediction of low-boom, supersonic aircraft.