Meta-modelling is a key technique for efficient multi-objective optimization in ship design projects using CFD. However, objective functions computed with CFD are not deterministic functions but contain random scatter about a smooth trend. Kriging is a meta-model technique that is well suited for numerical experiments with deterministic errors that can be perceived as random scatter due to varying input parameters. Simple Kriging, universal Kriging and polynomial regression are used to obtain approximate Pareto-fronts from the hull-form optimization of a chemical tanker including free-surface effects. Cross-validation is used to assess the quality of the meta-models and the meta-model approximations of the Pareto-fronts are verified. It is found that cross-validation can be used to select the best meta-model but should not be used to estimate the true error of the approximation in case the design of experiment is too coarse. The approach is used in practice in order to accelerate the ship design process and to obtain more efficient ships with less vibration hindrance.