Abstract: Superconductors are described by minimizers of the Ginzburg-Landau energy, which can exhibit fascinating macroscopic phenomena such as the formation of Abrikosov vortex lattices under an external magnetic field. The numerical approximation of these states is challenging due to stringent requirements on the computational mesh resolution, which can be expressed mathematically by error bounds of the discrete minimizers involving the mesh size and a material parameter in the Ginzburg-Landau energy functional. In this work, we present a framework based on Localized Orthogonal Decomposition, a multiscale technique for constructing problem-adapted approximation spaces. Tailored to the Ginzburg-Landau setting, this approach relaxes the mesh size and material parameter resolution constraints compared to standard finite element methods, allowing for more efficient and accurate approximations of vortex lattice structures in superconductors.