This article introduces a new and generalized approach to designing stacked patch antennas with responses of any order using a generalized circuit model assisted with multiple lump ports. The proposed method incorporates frequency-dependent K-inverters to account for the frequency-dependent radiating characteristics of the radiators. The design process begins with a preliminary configuration developed from a coupling matrix synthesized in accordance with specified design requirements. Subsequently, a circuit model is established based on this configuration, and the circuit parameters linked to this structure are captured through the use of space mapping technology, emphasizing the applicability of the circuit model. Iterative tuning, involving circuit-based “optimization on the fly,” is employed in the electromagnetic model to achieve better matching performance and desired radiation characteristics. It is remarkable that the duality of the circuit model is utilized in an analytical method for predicting the radiating performance of the patch antenna. This application of the dual circuit models, which embodies significant physical properties, represents a novel approach to antenna analysis. A fourth-order antenna prototype is constructed from a synthesized coupling matrix with a new circuit topology, and a new ring-shaped resonator is applied in that realization. The results obtained from the proposed design procedures, utilizing computer-aided techniques, demonstrate the successful design of stacked patch antennas with arbitrary-order frequency responses in a deterministic fashion. This approach offers a versatile and efficient method for designing complex antennas to meet specific design requirements.