The synthesis of multilayer wide-angle impedancematching (WAIM) structures for waveguide-fed planar phased array antennas is addressed. Under multifrequency constraints and assuming arbitrary array layouts, the synthesis problem is formulated within the system-by-design (SbD) framework. An iterative strategy is implemented by combining a fast EM modeling tool for the computation of the voltage reflection coefficient at the array surface and a solution-space sampling loop driven by the set of physical constraints describing both the synthesis objectives and the range boundaries for the degrees-of-freedom (DoFs) of the problem at hand. Thanks to the effectiveness and the reliability of such an integrated approach, it is possible to deal with multilayer multifrequency WAIM structures with uniaxially anisotropic permittivity and permeability tensors. Selected numerical results are presented to assess the potentialities and the reliability of the proposed approach also in comparison with state-of-the-art techniques