The growing field of superconducting technology is witnessing remarkable advancements driven by the global energy transition. These advancements bear significance, offering promising avenues for optimizing the design and performance of superconducting systems modeled by homogenized technique and/or thin strip approximation, including electrical machines, fusion energy generation, fault current limiters, superconducting cables, and superconducting maglev trains. This article introduces a thin strip homogenizing approximation and a versatile constraint methodology tailored for analyzing series, parallel, or series-parallel connections within superconducting devices. Leveraging the J-A formulation, comprehensive modeling of coils, stacks, thin strips, racetracks, and double crossed loops (DCLs) is undertaken to validate the proposed methodologies. Through meticulous investigations, encompassing analyses of magnetic flux density, current density distribution, current profiles, and losses, the efficacy and applicability of the proposed techniques are demonstrated.