The rate at which a once-abundant population declines in density prior to local or global extinction can strongly influence the precision of statistical estimates of extinction time. Here we report the development of a new, robust method of inference which accounts for these potential biases and uncertainties, and test it against known simulated data and dated Pleistocene fossil remains (mammoths, horses andNeanderthals). Our method is a Gaussian-resampled, inverse-weighted McInerny et al. (GRIWM) approach which weights observations inversely according to their temporal distance from the last observation of a species' confirmed occurrence, and for dates with associated radiometric errors, is able to sample individual dates from an underlying fossilization probability distribution. We show that this leads to less biased estimates of the 'true' extinction date. In general, our method provides a flexible tool for hypothesis testing, including inferring the probability that the extinctions of pairs or groups of species overlap, and for more robustly evaluating the relative likelihood of different extinction drivers such as climate perturbation and human exploitation.