With the increasing complexity of microwave and millimeter wave integrated circuits, the understanding and modeling of proximity coupled passive components and microstrip junctions play an important role in accurately predicting the circuit performance. In the research proposed in this document, a dynamic dispersive rigorous approach based on solving integral equations with numerical methods will be applied to a class of important microstrip junctions and transitions frequently encountered in integrated circuit structures. The research will also investigate theoretically and experimentally the issue of interconnects with emphasis on microwave and millimeter wave integrated circuit applications. It will focus initially on microstrip interconnects; the modelling and experimentation of multilevel collinear and transversely coupled interconnects in a substrate-super-strate configuration with the intent of optimizing the power coupled from one circuit level to another. Subsequently, multi- level cross-over interconnects will be studied with the intent of minimizing cross-talk as for VLSI applications, or maximizing coupling of power for certain integrated circuit microstrip antenna array applications. This will be subsequently expanded to deal with multiple or arrays of multi-level microstrip inter-connects in collinear, transverse as well as cross-over configurations. The issue of optical interconnects will also be addressed for dielectric waveguiding structures in a similar way as for microwave and millimeter wave circuits.