Abstract: The inability to correctly resolve rumours circulating online can have harmful real-world consequences. We present a method for incorporating model and data uncertainty estimates into natural language processing models for automatic rumour verification. We show that these estimates can be used to filter out model predictions likely to be erroneous so that these difficult instances can be prioritised by a human fact-checker. We propose two methods for uncertainty-based instance rejection, supervised and unsupervised. We also show how uncertainty estimates can be used to interpret model performance as a rumour unfolds.