Optimal sizing of analog circuits is a hard and time-consuming challenge. Nowadays, analog designers are more than ever interested in developing solutions for automating such a task. In order to overcome well-known drawbacks of the conventional equation-based and simulation-based sizing techniques, analog designers are being attracted by the so-called metamodeling techniques and recently have used them for establishing accurate models of circuits’ performances. Metamodels have been associated to optimization routines to maximize circuits’ performances. In this work we deal with the newly proposed efficient global optimization (EGO) algorithm that intrinsically offers both the metamodel generation and the optimization routine. Furthermore, it performs the requested task by using a relatively very small number of performance evaluations. Firstly, we focus on the convergence rates of the EGO technique via twenty benchmark test problems. Then, we use EGO for the optimal design of a couple of analog CMOS circuits. Comparison between EGO performances and those obtained using two surrogate-assisted metaheuristics is provided to show potentialities of the proposed approach. Finally, The case of muti-objective problems is also considered. The multi-objective efficient global optimization algorithm is used for generating Pareto fronts of conflicting perormances of two analog circuits. Obtained results are compared to those of the conventional in-loop optimization technique.