Next-generation electrolytes for lithium batteries must be able to conduct ions at sufficiently high current densities; yet this regime is rarely studied directly. The limiting current density of an electrolyte quantifies the highest possible rate of ion transport under an applied dc potential. Herein, we report on the limiting current density in twelve nanostructured polystyrene-block-poly(ethylene oxide) (PS-b-PEO, or SEO) copolymer electrolytes. We find that the limiting current at a given salt concentration increases systematically with increasing volume fraction of the PEO block (φEO). In contrast, the effective-medium theory, commonly used to analyze conductivity in block copolymer electrolytes, predicts that limiting current is independent of φEO. To resolve this conundrum, the ionic conductivity, the mutual diffusion coefficient of the salt, and the steady-state current fraction of the block copolymer electrolytes were measured. These measurements enable predictions of limiting current with no adjustable parameters using the concentrated solution theory. We found quantitative agreement between experimentally measured limiting current densities and predictions based on the concentrated solution theory. This work sheds light on how to reliably measure and predict limiting current density in composite electrolytes.