In the field of the Design and Analysis of Computer Experiments (DACE) meta-models are used to approximate time-consuming simulations. These simulations often contain simulation-model errors in the output variables. In the construction of meta-models, these errors are often ignored. Simulation-model errors may be magnified by the meta-model. Therefore, in this paper, we study the construction of Kriging models that are robust with respect to simulation-model errors. We introduce a robustness criterion, to quantify the robustness of a Kriging model. Based on this robustness criterion, two new methods to find robust Kriging models are introduced. We illustrate these methods with the approximation of the Six-hump camel back function and a real life example. Furthermore, we validate the two methods by simulating artificial perturbations. Finally, we consider the influence of the Design of Computer Experiments (DoCE) on the robustness of Kriging models.