The transmission line (TL) model has been used for decades to describe the propagation of signals and power along conducting wires. It is also well-known that it is based on the quasi-transverse electromagnetic (TEM) propagation hypothesis and is only accurate if the distance between the conductors is much smaller simultaneously than their length and the smallest characteristic wavelength of the signals. On the other hand, when these hypotheses are not matched, adopting full-wave methods for studying conductor bundles is not feasible due to the computational complexity of the resulting models. A compromise solution must be sought to represent electromagnetic phenomena more accurately without incurring an intractable computational complexity. Many approaches have been proposed over the years to handle this problem. In this work, we aim to extend to N-conductor TLs a specific method that is elegant and rigorous but currently limited to two-conductor TLs. This allows to model more rigorously 3-D effects such as propagation when the hypotheses of the standard TL theory are no longer matched. At the same time, the resulting model preserves the simplicity of 1-D models and is well suited to be integrated with 3-D models, since it will assume infinity as a reference. As a further outcome, the proximity effect is modeled by resorting to a harmonic expansion of the charge density. The proposed method is validated through three case studies. In particular, it is highlighted that it returns the standard model results when the assumptions underlying the “standard” model of TLs are satisfied. In contrast, it returns different results at high frequencies when the standard model is no longer adequate.