A method of uncertainty quantification in the calculation of wait-time probability distributions in delayed supercritical systems is presented. The method is based on Monte Carlo uncertainty quantification and makes use of the computationally efficient gamma distribution method for prediction of the wait-time probability distribution. The range of accuracy of the gamma distribution method is examined and parameterised based on the rate and magnitude of the reactivity insertion, the strength of the intrinsic neutron source and the prompt neutron lifetime. The saddlepoint method for inverting the generating function and a Monte Carlo simulation are used as benchmarks against which the accuracy of the gamma distribution method is determined. Finally, uncertainty quantification is applied to models of the Y-12 accident and experiments of Authier et al. (2014) on the Caliban reactor.