The objective of the paper is to present a general model for the coupling of antenna fields to lossy in-circuit interconnects such as striplines and interequipment interconnects such as braided coaxial cables, when the line is placed in the near-field zone of the antenna and the fields are highly non-uniform. The aim is to develop a general and fast algorithm for the line response which can be applied to any form of transmission line given the line geometry, type of the line and model for the antenna fields. Because of the complicated nature of the field distributions the actual coupling field calculations involve complex integrals and numerical procedures are employed to obtain the final results. Several antenna field distributions in different zones are considered and the numerical procedures adopted for the coupled field calculations are given in detail.