Meta-models proved to be a very efficient strategy for optimization of expensive black-box models, e.g. Finite Element simulation for electromagnetic devices. It enables to reduce the computational burden for optimization purposes but the conventional approach of using meta-models presents some limitations. Combining meta-models with a branch and bound strategy will lead to high fidelity global solutions. But, the efficiency of these algorithms relies on the estimation of the bounds. In this work, we investigated the prediction error given by meta-models to apply such approach and applied it to electromagnetic benchmark problems.