In this paper, the performance of the Bayesian Optimization (BO) technique applied to various problems of microwave engineering is studied. Bayesian optimization is a novel, non-deterministic, global optimization scheme that uses machine learning to solve complex optimization problems. However, each new optimization scheme needs to be evaluated to find its best application niche, as there is no universal technique that suits all problems. Here, BO was applied to different types of microwave and antenna engineering problems, including matching circuit design, multiband antenna and antenna array design, or microwave filter design. Since each of the presented problems has a different nature and characteristics such as different scales (i.e. number of design variables), we try to address the question about the generality of BO and identify the problem areas for which the technique is or is not recommended.