Projections of future climate change to support decision-making require Earth system models (ESMs) running at high spatial resolution, but this is computationally prohibitive. A major challenge is the calibration (parameter tuning) during the development of ESMs, which requires running large numbers of simulations to identify the optimal values for parameters that are poorly constrained by observations. Here we train a convolutional neural network (CNN) on perturbed parameter ensembles from two lower-resolution (and thus much less expensive) versions of the same ESM, and a smaller number of higher-resolution simulations. Cross-validated results show that the CNN’s skill exceeds that of a climatological baseline for most variables with as few as 5-10 examples of the higher-resolution ESM, and for all variables (including precipitation) with at least 20 examples. This proof-of-concept study offers the prospect of significantly more efficient calibration of ESMs, by reducing the required CPU time for calibration by 20-40 \%