Approximation-based hybrid algorithms are a class of algorithms that employ local approximations in the local search phase of the optimization process. The local search is an important phase in the optimization process since it may represent a significant overhead in expensive-to-evaluate problems, as is the case in electromagnetic design. The hybrid algorithm should converge in less time than the conventional algorithm, in order to be useful in practice. In this work, we present a thorough analysis of the computational cost involved in approximation-based hybrid algorithms. We illustrate our analysis by comparing the performance of the conventional and hybrid algorithms in an analytical problem and in the design of the shape of the pole face of a magnetizer.