The stratospheric polar vortex critically influences wintertime stratospheric circulation, as well as troposphere-stratosphere coupling and trace gas distribution. Reproducing correct statistics of stability and strength of the polar vortex is an important challenge for Earth system models as its variability affects regional climate predictability. The latest generation of the models are showing pronounced biases and intermodel spread in this regard. Here, we show how parameterized orographic gravity wave drag (OGWD) in climate models modulates planetary wave propagation, impacting SPV stability and morphology. We analyze simulations from 14 models produced within the Coupled Model Intercomparison Project Phase 6 (CMIP6). The orographic gravity wave drag varies between the models, depending on a parameterization scheme and the tuning of free parameters. We investigate how the intermodel differences in the parameterized gravity wave drag in the upper troposphere lower stratosphere relate to resolved wave activity and SPV characteristics. We find that stronger OGWD suppresses upward planetary wave propagation, leading to reduced wave breaking at the SPV edge and a more stable, broader vortex. By documenting the role of the orographic gravity wave drag for the boreal stratospheric polar vortex in the models, we highlight the potential of improvements or careful tuning of this parameterization for alleviating the climate model biases related to polar vortices.