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This article presents a fundamental strategy for accurately modeling the mutual coupling of arbitrary order in any large-scale electromagnetic structures and high-density integrated chips such as antenna array elements and coupled circuit elements. The proposed method starts from the modeling of the first-order mutual coupling, and it consists of two main steps. First of all, an equivalent circuit model describing low-order mutual coupling (adjacent coupling) is characterized and established, of which each parametric value is accurately extracted by making use of a numerical calibration technique. Then, the circuit model for high-order mutual coupling (crossover or crosstalk coupling) is generated from the lower order models, and it can further be used for the modeling of mutual coupling of any higher order. The accuracy and efficiency of the proposed method are demonstrated by three different kinds of structure including a linear phased array antenna, a finite periodic electromagnetic structure, and a planar low-pass filter. This novel approach represents an easy, fast, and effective characterization of arbitrary-order mutual coupling. It can find applications in the modeling of mutual coupling between any circuit elements and building blocks such as antennas, resonators, and even small discontinuities, and it promises to be helpful for the analysis and iterative design of microwave circuits and antenna arrays. © 2010 Wiley Periodicals, Inc. Int J RF and Microwave CAE, 2011. [ABSTRACT FROM AUTHOR]