Abstract This study evaluates the representation of the composite-mean surface response to sudden stratospheric warmings (SSWs) in 28 CMIP6 models. Most models can reproduce the magnitude of the SLP response over the Arctic, although the simulated Arctic SLP response varies from model to model. Regarding the structure of the SLP response, most models exhibit a basin-symmetric negative Northern Annular Mode (NAM)-like response with a cyclonic Pacific SLP response, whereas the reanalysis shows a highly basin-asymmetric negative NAO-like response without a robust Pacific center. We then explore the drivers of these model biases and spread by applying a multiple linear regression (MLR). The results show that the polar cap temperature anomalies at 100 hPa (ΔT100) modulate the magnitude of both the Arctic SLP response and the cyclonic Pacific SLP response. Apart from ΔT100, the intensity and latitudinal location of the climatological eddy-driven jet in the troposphere also affect the magnitude of the Arctic SLP response. The compensation of model biases in these two tropospheric metrics and the good model representation of ΔT100 explain the good agreement between the ensemble mean and the reanalysis on the magnitude of the Arctic SLP response, as indicated by the fact that the ensemble mean lies well within the reanalysis uncertainty range and that the reanalysis mean sits well within the model distribution. The Niño-3.4 SST anomalies and North Pacific SST dipole anomalies together with ΔT100 modulate the cyclonic Pacific SLP response. In this case, biases in both oceanic drivers work in the same direction and lead to the cyclonic Pacific SLP response in models that are not present in the reanalysis. Significance Statement Sudden stratospheric warmings (SSWs) represent an important source of skill for forecasting winter weather on subseasonal-to-seasonal time scales. To what extent SSWs could be used to improve the prediction of surface weather depends on how well stratosphere–troposphere coupling associated with SSWs is represented in climate models. Therefore, we evaluate the representation of stratosphere–troposphere coupling associated with SSWs in 28 state-of-the-art climate models. The representation is found to diverge widely among climate models, and some are biased noticeably from the reanalysis. The models’ spread and bias are largely driven by five major factors and can be reduced substantially by making bias corrections to these factors.