An automated optimization process for designing and optimising high-performance single microstrip antennas is presented. It consists of the successive use of two optimization methods, bottom-up optimization (BUO) and Bayesian optimization (BO), which are applied sequentially, resulting in electromagnetic (EM)-based artificial neural network modelling. The BUO method is applied for the initial design of the structure of the antennas whereas the BO approach is successively implemented to predict suitable dimensional parameters, leading to broadband, high flat-gain antennas. The optimization process is performed automatically with the combination of an electronic design automation tool and a numerical analyser. The proposed method is easy to use; it allows one to perform the design with little experience, because both structure modelling and sizing are performed automatically. To verify the power of the proposed EM-based method experimentally, two single microstrip antennas have been designed, optimised, fabricated, and measured. The first antenna has flat-gain performance (6.9-7.2 dB) in a frequency band of 8.8-10 GHz. The second has been designed to perform in the 8.7- to 10-GHz band, where it exhibits flat-gain performance with reduced fluctuation in the range of 6.7-7 dB. The experimental results are in good agreement with the numerical data.