Optimizing complex engineering problems may demand large computational efforts because of the use of numerical models. Global optimization can be established through the use of evolutionary algorithms, but may demand a prohibitive amount of computational time. In order to reduce the computational time, we incorporate in the global optimization procedures a physics-based fast coarse model. This paper presents a two-level genetic algorithm (2LGA) for electromagnetic optimization. This algorithm employs the global convergence properties of the genetic algorithm, where acceleration of the optimization results from the fast computations of the coarse model (low level) and where accuracy is guaranteed by using a limited number of fine model (high level) evaluations. Using the coarse model, we iteratively build surrogate models (intermediate levels) where metamodels produce surrogate models which approximate the fine model. The proposed algorithm comprises internal parameters which are self-tunable. We applied the 2LGA to the optimization of an algebraic test function, to the optimization of a die press model (TEAM Workshop Problem 25) and to the optimization of an octangular double-layered electromagnetic shield. The results show that the 2LGA is converging to the optimal solutions as the traditional genetic algorithm and that the acceleration is dependent on the accuracy of the low level. An acceleration factor of more than two can be achieved.