Faithful representations of atomic environments and general models for regression can be harnessed to learn electron densities that are close to the ground state. One of the applications of data-derived electron densities is to orbital-free density functional theory. However, extrapolations of densities learned from a training set to dissimilar structures could result in inaccurate results, which would limit the applicability of the method. Here, we show that a non-Bayesian approach can produce estimates of uncertainty which can successfully distinguish accurate from inaccurate predictions of electron density. We apply our approach to density functional theory where we initialise calculations with data-derived densities only when we are confident about their quality. This results in a guaranteed acceleration to self-consistency for configurations that are similar to those seen during training and could be useful for sampling based methods, where previous ground state densities cannot be used to initialise subsequent calculations.