One strategy to overcoming the slow kinetics associated with electrochemical magnesium ion storage is to employ a permanently porous, capacitive cathode material together with magnesium metal as the anode. This strategy has begun to be employed, for example, using framework solids like Prussian blue analogs, or porous carbons derived from metal-organic frameworks, but the cycling stability of an ordered, bottom-up synthesized, three-dimensional carbon framework toward magnesiation and demagnesiation in a shuttle-type battery remains unexplored. Zeolite-templated carbons (ZTCs) are a class of ordered porous carbonaceous framework materials with numerous superlative properties relevant to electrochemical energy storage. Herein, we report that ZTCs can serve as high-power cathode materials for magnesium-ion hybrid capacitors (MHCs), exhibiting high specific capacities (e.g., 113 mAh g-1 after 100 cycles) with an average discharge voltage of 1.44 V and exceptional capacity retention (e.g., 76% after 200 cycles). ZTC-based MHCs meet or exceed the gravimetric energy densities of state-of-the-art batteries functioning on the Mg2+ shuttle, while simultaneously displaying far superior rate-capabilities (e.g., 834 W kg-1 at 600 mA g-1).