Numerical methods are used to simulate the mathematical models of a wide range of engineering problems. The precision provided by such simulators is usually fine but at the price of computational cost. In some applications this cost might be crucial. This leads us to consider cheap surrogate models in order to reduce the computation time still meeting the precision requirements. Among all available surrogate models, we deal herein with the generation of an ?optimal? database of pre-calculated results combined with a simple interpolator. A database generation approach is investigated which is intending to achieve an optimal sampling. Such databases can be used for the approximate solution of both forward and inverse problems. Their structure carries some meta-information about the involved physical problem. In the case of the inverse problem, an approach for predicting the uncertainty of the solution (due to the applied surrogate model and/or the uncertainty of the measured data) is presented. All methods are based on kriging ---a stochastic tool for function approximation. Illustrative examples are drawn from eddy-current nondestructive evaluation.