The favourable properties of tungsten borides for shielding the central High Temperature Superconductor (HTS) core of a spherical tokamak fusion power plant are modelled using the MCNP code. The objectives are to minimize the power deposition into the cooled HTS core, and to keep HTS radiation damage to acceptable levels by limiting the neutron and gamma fluxes. The shield materials compared are W2B, WB, W2B5 and WB4 along with a reactively sintered boride B0.329C0.074Cr0.024Fe0.274W0.299, monolithic W and WC. Of all these W2B5 gave the most favourable results with a factor of ~10 or greater reduction in neutron flux and gamma energy deposition as compared to monolithic W. These results are compared with layered water-cooled shields, giving the result that the monolithic shields, with moderating boron, gave comparable neutron flux and power deposition, and (in the case of W2B5) even better performance. Good performance without water-coolant has advantages from a reactor safety perspective due to the risks associated with radio-activation of oxygen. 10B isotope concentrations between 0 and 100% are considered for the boride shields. The naturally occurring 20% fraction gave much lower energy depositions than the 0% fraction, but the improvement largely saturated beyond 40%. Thermophysical properties of the candidate materials are discussed, in particular the thermal strain. To our knowledge, the performance of W2B5 is unrivalled by other monolithic shielding materials. This is partly as its trigonal crystal structure gives it higher atomic density compared with other borides. It is also suggested that its high performance depends on it having just high enough 10B content to maintain a constant neutron energy spectrum across the shield.