A novel Runaway Electron Mitigation Coil (REMC) is under development for the Tokamak à Configuration Variable (TCV) to enable passive prevention and deconfinement of relativistic runaway electrons (REs). This non-axisymmetric coil is designed to couple passively to the disruption-induced loop voltage during the current quench phase, generating large non-axisymmetric fields that destroy magnetic flux surfaces and deconfine the RE population. The REMC aims to drive an n = 1 perturbation while maximizing inductive coupling to the plasma, thereby inducing significant current in the coil. It will represent the first passive coil installed on a tokamak with a robust runaway electron scenario. A comprehensive modeling workflow supports the coil design, combining 3D electromagnetic modeling with MHD plasma response analysis. The ThinCurr electromagnetic model is used to explore various coil configurations within realistic machine constraints. This model incorporates detailed representations of the vacuum vessel and other conducting structures, accounting for material resistivities, and enables evaluation of both induced coil currents and the resulting 3D magnetic field structures. Based on these vacuum criteria, the three most promising coil configurations are selected for further analysis using the linear MHD code MARS-F, which assesses the plasma response to the 3D field and its impact on relativistic test particles. Through experimental validation and comparison with modeling, this first-of-its-kind passive coil is expected to provide valuable insights into the REMC concept and its potential applicability in future reactor-scale devices.