The optimization of the efficiency of an ECR-based charge breeder is a twofold task: efforts must be paid to maximize the capture of the injected 1+ ions by the confined plasma and to produce high charge states to allow post-acceleration at high energies. Both tasks must be faced by studying in detail the electrons heating dynamics, influenced by the microwave-to-plasma coupling mechanism. Numerical simulations are a powerful tools for obtaining quantitative information about the wave-to-plasma interaction process: this paper presents a numerical study of the microwaves propagation and absorption inside the plasma chamber of the PHOENIX charge breeder, which the selective production of exotic species project, under construction at Legnaro National Laboratories, will adopt as charge breeder. Calculations were carried out with a commercial 3D FEM solver: first, all the resonant frequencies were determined by considering a simplified plasma chamber; then, the realistic geometry was taken into account, including a cold plasma model of increasing complexity. The results gave important information about the power absorption and losses and will allow the improvement of the plasma model to be used in a refined step of calculation reproducing the breeding process itself.