We estimate the propagation of uncertainties in electromagnetic wave scattering problems. The computational domain is a dielectric object with uncertain shape. Since classical Monte Carlo (MC) method is too expensive, we suggest to use a modified multilevel Monte Carlo (MLMC) method. This method uses a hierarchy of spatial meshes and optimally balances the statistical and discretisation errors. MLMC performs most of the simulations using low-fidelity models and only a few simulations using high-fidelity models. As a result, the final computational cost is becoming significantly smaller.