The stratospheric northern annular mode (SNAM) describes winter variability in the strength of the stratospheric jet stream (or polar vortex). The structure and dynamics of SNAM in CMIP5 simulations are studied, emphasizing (i) stratosphere–troposphere linkages and (ii) differences between models with stratospheres that are either well represented (so-called high-top [HT] models) or poorly represented (low-top [LT] models). Unlike HT models, SNAM is too weak in the stratosphere for the LT models, consistent with weaker polar vortex variability.  However, this bias does not carry over to the impact of SNAM upon tropospheric jet stream variability, which is realistically represented in both HT and LT models. On the other hand, regional storm track and sea level pressure patterns induced by SNAM are anomalously weak and eastward shifted (compared to observations) for both model groups.  Dynamical analyses reveal that variability in stratospheric planetary wave activity is also reduced in LT models. This seems related to relatively weak vertical dynamical coupling in LT models.  More specifically, vertical Rossby wave propagation is anomalously weak above the tropopause in LT models, suggesting that weak polar vortex variability in LT models is due to the inability of tropospheric planetary wave activity to enter the stratosphere. Paradoxically, this deficiency appears to have little net impact upon the attendant tropospheric signature of SNAM events.