Results are reported on cemented tungsten carbide (cWC) and boride-containing composite materials for the task of shielding the centre column of a superconducting tokamak power plant. The shield is based on five concentric annular shells consisting of cWC and water layers of which the innermost cWC shield can be replaced with boride composites. Sample materials have been fabricated changing the parameters of porosity P, binder alloy fraction fbinder and boron weight fraction fboron. For the fabricated materials, and other hypothetical samples with chosen parameters, Monte Carlo studies are made of: (i) the power deposition into the superconducting core, (ii) the fast neutron and gamma fluxes and (iii) the attenuation coefficients through the shield for the deposited power and neutron and gamma fluxes. It is shown that conventional Co-based cWC binder alloy can be replaced with a Fe–Cr alloy (92 wt.% Fe, 8 wt.% Cr), which has lower activation than cobalt with minor changes in shield performance. Boride-based composite materials have been prepared and shown to give a significant reduction in power deposition and flux, when placed close to the superconducting core. A typical shield of cemented tungsten carbide with 10 wt.% of Fe–8Cr binder and 0.1% porosity has a power reduction half-length of 0.06 m. It is shown that the power deposition increases by 4.3% for every 1% additional porosity, and 1.7% for every 1 wt.% additional binder. Power deposition decreased by 26% for an initial 1 wt.% boron addition, but further increases in fboron showed only a marginal decrease. The dependences of power deposited in the core, the maximum neutron and gamma fluxes on the core surface, and the half attenuation distances through the shield have been fitted to within a fractional percentage error by analytic functions of the porosity, metallic binder alloy and boron weight fractions.