Refractory high-entropy alloys (RHEAs) with high melting points and low neutron absorption cross-section are sought for generation-IV fission and fusion reactors. A high throughput computational screening tool, Alloy Search and Predict (ASAP), was used to identify promising RHEA candidates from over 1 million four-element equimolar combinations. The selected VNbCrMo RHEA was further studied by CALPHAD to predict phase formation, which was compared to an experimentally produced ingot aged at 1200 °C. The VNbCrMo RHEA was found to constitute a majority bcc phase, with a 6% area fraction of C15-Laves formed at interdendritic regions, in contrast to the predictions of single-phase. The prediction of the yield strength by a model based upon edge dislocation mechanisms indicated 2.1 GPa at room temperature and 850 MPa at 1000 °C for the equimolar single bcc phase. The hardness of the alloy with C15-Laves was 748 HV (yield strength ~2.4 GPa). Finally, the macroscopic neutron absorption cross-section was modelled for a wide range of energies. Displacements per atom per year and activation calculations, up to 1000 years after 2 years of continuous operation, in typical fusion and fission reactor scenarios were also performed using the inventory code FISPACT-II. This work gives new insight into the phase stability and performance of the VNbCrMo RHEA, which is compared with a similar design concept alloy, to assess the potential of novel RHEAs for use in advanced nuclear applications.