The 11 year solar-cycle component of climate variability is assessed in historical simulations of models taken from the Coupled Model Intercomparison Project, phase 5 (CMIP-5). Multiple linear regression is applied to estimate the zonal temperature, wind and annular mode responses to a typical solar cycle, with a focus on both the stratosphere and the stratospheric influence on the surface over the period ∼1850–2005. The analysis is performed on all CMIP-5 models but focuses on the 13 CMIP-5 models that resolve the stratosphere (high-top models) and compares the simulated solar cycle signature with reanalysis data. The 11 year solar cycle component of climate variability is found to be weaker in terms of magnitude and latitudinal gradient around the stratopause in the models than in the reanalysis. The peak in temperature in the lower equatorial stratosphere (∼70 hPa) reported in some studies is found in the models to depend on the length of the analysis period, with the last 30 years yielding the strongest response. A modification of the Polar Jet Oscillation (PJO) in response to the 11 year solar cycle is not robust across all models, but is more apparent in models with high spectral resolution in the short-wave region. The PJO evolution is slower in these models, leading to a stronger response during February, whereas observations indicate it to be weaker. In early winter, the magnitude of the modelled response is more consistent with observations when only data from 1979–2005 are considered. The observed North Pacific high-pressure surface response during the solar maximum is only simulated in some models, for which there are no distinguishing model characteristics. The lagged North Atlantic surface response is reproduced in both high- and low-top models, but is more prevalent in the former. In both cases, the magnitude of the response is generally lower than in observations.