Abstract Large-ensemble climate model simulations can provide deeper understanding of the characteristics and causes of extreme events than historical observations, due to their larger sample size. However, adequate evaluation of simulated ‘unseen’ events that are more extreme than those seen in historical records is complicated by observational uncertainties and natural variability. Consequently, conventional evaluation and correction methods cannot determine whether simulations outside observed variability are correct for the right physical reasons. Here, we introduce a three-step procedure to assess the realism of simulated extreme events based on the model properties (step 1), statistical features (step 2), and physical credibility of the extreme events (step 3). We illustrate these steps for a 2000 year Amazon monthly flood ensemble simulated by the global climate model EC-Earth and global hydrological model PCR-GLOBWB. EC-Earth and PCR-GLOBWB are adequate for large-scale catchments like the Amazon, and have simulated ‘unseen’ monthly floods far outside observed variability. We find that the realism of these simulations cannot be statistically explained. For example, there could be legitimate discrepancies between simulations and observations resulting from infrequent temporal compounding of multiple flood peaks, rarely seen in observations. Physical credibility checks are crucial to assessing their realism and show that the unseen Amazon monthly floods were generated by an unrealistic bias correction of precipitation. We conclude that there is high sensitivity of simulations outside observed variability to the bias correction method, and that physical credibility checks are crucial to understanding what is driving the simulated extreme events. Understanding the driving mechanisms of unseen events may guide future research by uncovering key climate model deficiencies. They may also play a vital role in helping decision makers to anticipate unseen impacts by detecting plausible drivers.