We present the combination of the numerical 3D magnetic field simulation of SWISSCASE, the new 10 GHz ECR ion source at the University of Bern in Switzerland, and the experimental X-ray Bremsstrahlung measurement of the same ion source, to determine the hot electron and the total electron number densities of its ECR plasma. The results, which are in excellent agreement with literature, demonstrate the quality of the numerical simulation, the X-ray Bremsstrahlung measurement and the method of combination to calculate these particle densities. The revealed key parameters of the ECR plasma such as geometry, particle densities and Bremsstrahlung emission, may enable the development of a microwave ECR plasma model, yet to be defined, which can be integrated into a Finite Difference Time Domain (FDTD) simulation to reproduce realistic microwave-plasma interaction. The presented method of 3D magnetic field modeling, X-ray Bremsstrahlung measurement and the subsequent determination of the electron densities is not limited to the SWISSCASE ion source but can further be used for detailed investigation and optimization of current and future electric propulsion concepts.