The thesis considers mutual coupling between microstrip antennas with parasitic resonator, embedded in arbitrary planar multilayer dielectric structure. A rigorous method of analysis is described, where patch currents are expanded as a linear combination of basis functions and then the electric field integral equation is solved using method of moments. Entire domain basis functions are used, and their distribution over patch corresponds to the cavity resonator model of the patch. Moment method matrix and excitation matrix elements are calculated in spectral domain, and the properties of the Green's function in spectral domain are used to simplify the expressions that are calculated numerically. The procedure for the calculation of these matrix elements, which uses contour path modification in complex plane when performing inverse Fourier transformation is given in detail. The impedance and scattering matrices of the antenna array are determined and the procedure of the gain pattern calculation is given, using Green's functions in spectral domain when the amplitudes of basis functions are known. The synthesis procedure of the broadband microstrip antennas with parasitic resonator is described, and the reliability of optimisation using hybrid genetic algorithm is demonstrated on an example of circularly polarised broadband microstrip antenna. The developed software is used to show and analyse the mutual coupling of broadband microstrip antennas with parasitic resonator. A broadband stacked microstrip antenna of optimised dimensions is found, and applied as an array element in the experimental model. Thorough measurements of mutual coupling between two such elements in both E- and H- plane are carried out, and the experimental results were compared with the results obtained by calculation. Furthermore, the contribution of surface and space waves to the magnitude of mutual coupling is analysed. Using developed software, some cases from literature with available data of mutual coupling measurements are analysed and the comparison between measured and calculated data is given. In all cases where comparison between measurements and calculation was performed, good agreement in the results was observed.