The predictability of the Northern Hemisphere stratosphere and its underlying dynamics are investigated in five state-of-theart seasonal prediction systems from the Copernicus Climate Change Service (C3S) multi-model database. Special attention is devoted to the connection between the stratospheric polar vortex (SPV) and lower-stratosphere wave activity (LSWA). We find that in winter (December to February) dynamical forecasts initialised on the first of November are considerably more skilful than empirical forecasts based on October anomalies. Moreover, the coupling of the SPV with mid-latitude LSWA (i.e., meridional eddy heat flux) is generally well reproduced by the forecast systems, allowing for the identification of a robust link between the predictability of wave activity above the tropopause and the SPV skill. Our results highlight the importance of November-to-February LSWA, in particular in the Eurasian sector, for forecasts of the winter stratosphere. Finally, the role of potential sources of seasonal stratospheric predictability is considered: we find that the C3S multi-model overestimates the stratospheric response to El Niño-Southern Oscillation (ENSO) and underestimates the influence of the Quasi-Biennial Oscillation (QBO).