Microwave circuits are an efficient means for physically implementing coherent quantum systems, notably using superconductive devices at millikelvin temperatures. However, classical microwave theory is insufficient to describe circuit behavior at the quantum level. Quantum noise, for instance, corrupts information within the internal states of a circuit at the single-photon level. A theoretical infrastructure to account for quantum effects has been established as quantum input-output network (QION) theory, which is within the framework of quantum optics. In this work, we consider how an extension to QION theory, known as SLH theory, extends quantum stochastic differential equations to multi-port networks. A mathematical object comprised of three matrices, known as an SLH triple, may then describe full network dynamics. SLH theory is applicable to a variety of multi-interdisciplinary subfields within physics and engineering. This thesis will cover how universal multi-port network design is accomplished using SLH formalism, and how this can be applied to microwave engineering in the quantum limit.