This thesis investigates the electromagnetic response of thin-film type-II superconductors as measured by a Stiffnessometer. While this device provides a highly sensitive probe of superconducting phase stiffness, extracting fundamental material properties from its readings requires overcoming significant theoretical and computational challenges. Specifically, standard analytical approximations and commercial finite-element solvers fail to accurately resolve the highly non-linear Ginzburg-Landau equations in the extreme ultra-thin ring limit. To address this gap, this work develops a dedicated numerical framework based on the one-dimensional Squared-Operator Method (SOM). By generating continuous, artifact-free theoretical universal curves, this customized approach successfully bridges the gap between the physical experimental response and the mathematical model. Ultimately, this robust framework want to provides the necessary tools for accurately decoding Stiffnessometer data, enabling the precise extraction of critical superconducting length scales, primarily the Pearl length (Λ) and the coherence length (ξ). Joint work with Amit Keren Advisor: Prof. Nir Gavish