In this study, we investigate the high-frequency limits of artificial dielectrics in the context of gradient index (GRIN) lens antennas. We provide an overview of general GRIN media structures and introduce three factors which determine lens frequency limits: 1) permittivity profile discretization; 2) unit cell (UC) lattice constant Lc ; and 3) surface impedance matching layer thickness, Δzmatch . Multimodal eigenmode analysis is performed for two common GRIN media UCs, the cubic gyroid, and the hexagonal drilled substrate. Soft- and hard-cutoff frequency limits ( fsc and fhc ) are defined, and the corresponding lattice constant size limits are provided as Lsc<(2–√)/2λg,eff and Lhc<(3–√)/2λg,eff . These limits are validated with 3-D-printed spherical Luneburg lenses having various lattice constants and a low-profile 3-D-printed cylindrical GRIN lens using multiple materials and having a large permittivity range. The results in this work enable designers to use the simplest possible UC for GRIN media realization while guaranteeing performance at a desired frequency. This not only improves performance but also saves cost by obviating the need for overly conservative approximations.