TaC, HfC and their solid solutions are promising candidate materials for thermal protection structures in hypersonic vehicles because of their very high melting temperatures (>4000 K) among other properties. The melting temperatures of slightly hypostoichiometric TaC, HfC and three solid solution compositions (Ta1-xHfxC, with x = 0.8, 0.5 and 0.2) have long been identified as the highest known. In the current research, they were reassessed, for the first time in the last fifty years, using a laser heating technique. They were found to melt in the range of 4041-4232 K, with HfC having the highest and TaC the lowest. Spectral radiance of the hot samples was measured in situ, showing that the optical emissivity of these compounds plays a fundamental role in their heat balance. Independently, the results show that the melting point for HfC0.98, (4232 ± 84) K, is the highest recorded for any compound studied until now.