Uncertainty quantification of weather forecasts is a necessity for reliably planning for and responding to extreme weather events in a warming world. This motivates the need for well-calibrated ensembles in probabilistic weather forecasting. We present initial results for the calibration of large-scale deep neural weather models for data-driven probabilistic weather forecasting. By explicitly accounting for uncertainties about the forecast's initial condition and model parameters, we generate ensemble forecasts that show promising results on standard diagnostics for probabilistic forecasts. Specifically, we are approaching the Integrated Forecasting System (IFS), the gold standard on probabilistic weather forecasting, on: (i) the spread-error agreement; and (ii) the Continuous Ranked Probability Score (CRPS). Our approach scales to state-of-the-art data-driven weather models, enabling cheap post-hoc calibration of pretrained models with tens of millions of parameters and paving the way towards the next generation of well-calibrated data-driven weather models.