Local, bulk response functions, e.g. permittivity, and the macroscopic Maxwell equations completely specify the classical electromagnetic problem, which features only wavelength λ and geometric scales. The above neglect of intrinsic electronic length scales L e leads to an eventual breakdown in the nanoscopic limit. Here, we present a general theoretical and experimental framework for treating nanoscale electromagnetic phenomena. The framework features surface-response functions-known as the Feibelman d-parameters-which reintroduce the missing electronic length scales. As a part of our framework, we establish an experimental procedure to measure these complex, dispersive surface response functions, enabled by quasi-normal-mode perturbation theory and observations of pronounced nonclassical effects-spectral shifts in excess of 30% and the breakdown of Kreibig-like broadening-in a quintessential multiscale architecture: film-coupled nanoresonators, with feature-sizes comparable to both L e and λ.