Abstract. Future sea surface temperature and sea-ice concentration from coupled ocean–atmosphere general circulation models such as those from the CMIP5 experiment are often used as boundary forcings for the downscaling of future climate experiments. Yet, these models show some considerable biases when compared to the observations over present climate. In this paper, existing methods such as an absolute anomaly method and a quantile–quantile method for sea surface temperature (SST) as well as a look-up table and a relative anomaly method for sea-ice concentration (SIC) are presented. For SIC, we also propose a new analogue method. Each method is objectively evaluated with a perfect model test using CMIP5 model experiments and some real-case applications using observations. We find that with respect to other previously existing methods, the analogue method is a substantial improvement for the bias correction of future SIC. Consistency between the constructed SST and SIC fields is an important constraint to consider, as is consistency between the prescribed sea-ice concentration and thickness; we show that the latter can be ensured by using a simple parameterisation of sea-ice thickness as a function of instantaneous and annual minimum SIC.