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Microstrip transmission lines in the proximity of each other are not always in parallel directions. In this paper, a fast method is proposed to determine the coupling of the external incident fields on the terminals of orthogonal interconnections embedded in multilayered media in the 1- 20 GHz frequency range. Because of the weak coupling between the lines, the effect of the incident plane wave is studied by applying standard Baum-Liu-Tesche equations separately for each interconnection. Later, the coupling between the lines is applied to terminal voltages by the use of a predetermined capacitance circuit model of the cross region. The experimental validation is also presented to verify the obtained results.