Uncertainty quantification (UQ) of spent nuclear fuel (SNF) is a crucial task that provides predictions and confidence bounds for important quantities of interest, such as decay heat, nuclide content, or k-effective. An accurate estimation of these quantities and their uncertainties is essential to reduce the risks and costs of storing and transporting SNF. The most accurate and robust method employed in reactor physics computations for UQ is Monte Carlo, however it is computationally intensive, to the point where it is unfeasible to carry out UQ for all the high-level waste expected in Switzerland. In this work, Multifidelity Monte Carlo (MFMC) is applied for the first time to the UQ of SNF, and a novel model management strategy to alleviate the training costs of MFMC is introduced. It is shown that MFMC drastically reduces the computational costs of UQ, with speedups between 5 and 1500 with respect to simple Monte Carlo.