Nowadays, computational systems are demanding high performance operating frequencies with a high-density interconnect (HDI) scheme. As a result the impact of the common-mode noise present in these systems in the signal integrity has become a major concern. Differential interconnects have demonstrated to be a reliable solution due to its property of being less susceptible to this type of noise. Nevertheless, these interconnects consists of two signal traces to carry the data with an electromagnetic coupling between them. For this reason, studying the coupling between the signal traces is mandatory these days for optimizing the corresponding interconnects. Moreover, it is of great interest to study the coupling mechanisms between these two signal traces and how it can be modeled with lumped circuits. In this regard, the purpose of this thesis is to propose new methodologies to implement equivalent circuit models in commercial circuit simulators, with their corresponding parameters extraction processes for this interconnects. Consequently, a new topology for the characterization of a differential launch structure and the implementation of a model for the homogeneous part of a differential transmission line which considers the effect of the current distribution in the inductance of the line are presented as a result of this thesis. Chip design as well as fabrication technologies have experienced a tremendous evolution in recent years allowing the transmission of data at very high data rates within the tens of Gbps. Thus, the losses associated to a transmission line are reaching unacceptable levels letting current high-speed electronic systems unable to handle higher frequencies signals, becoming these interconnects the bottleneck when designing high-speed interconnection channels. For this reason, electronic systems performance at high frequencies has to improve by identifying the effects that negatively influence the corresponding electrical performance. In order to this, equivalent circuit models for differential transmission lines used in complex devices such as HDI PCBs or packages can be used in the analysis to carry out an optimization of the interconnection channel.