Abstract High amplitude quasi-stationary Rossby waves (QSWs) have been connected to extreme weather events. By identifying particularly high amplitude QSW events (QWEs) over Europe and North America we study their characteristics in ERA5 re-analysis data and in ensemble simulations from the CESM2 general circulation model. The CESM2 reproduces the overall statistics of QWEs, with ERA5 results within the ensemble spread. The ensemble spread is large, indicating a strong influence of internal variability. Composites of meridional wind anomalies for QWEs show a phase preference in both ERA5 and CESM2, resembling the climatological wave pattern. This is partly due to the definition of QSWs; with the day-of-year climatological meridional wind removed when identifying QSWs, the phase preference remains, albeit with a weaker signal. Significant tropical Pacific precipitation anomalies are seen 5-15 days before observed QWEs; the location of these anomalies is broadly reproduced in CESM2, but the magnitude is substantially underestimated and the time scale is biased. We find a narrowed and strengthened jet stream over the Pacific at the early stage of European QWEs, which may create enhanced waveguidability; this signal is generally reproduced in the models. Overall, the CESM2 can simulate QWEs; differences between the model ensemble mean and re-analysis could result from model bias or internal variability, although biases are not reduced in CESM2 simulations forced with observed SSTs.