We present the process and results of neutronics-driven shielding design using metal and ceramic matrix metal hydride neutron shields within the context of compact, high-power tokamaks. In particular, hafnium hydrides were considered within a matrix of stainless steel or magnesium oxide and contrasted with established and novel fast neutron shielding materials. These shielding materials are found to substantially increase the lifetime of toroidal field magnets made of high-temperature superconductors by a factor of up to 14.5. Specifically, a stainless steel–20% HfH1.7 thermal shield and outer neutron shield, paired with an inner tungsten carbide (WC) shield and toroidal field magnet case and winding pack both doped with 40% HfH1.7 by volume, were found to achieve a 93.1% reduction in peak fast neutron flux to high-temperature superconductor tapes. Simultaneously, this configuration reduced the total mass (and cost) of the neutron shield, as well as the nuclear heating rate of the magnet coil, in comparison to monolithic shields of WC and boron carbide.