Bond characteristics, mechanical properties, and high-temperature thermal conductivity of ultrahigh-temperature ceramics (UHTCs), hafnium carbide (HfC), tantalum carbide (TaC), and their solid solution composites, were investigated using first-principles calculations. Mulliken analyses revealed that Ta formed stronger covalent bonds with C than did Hf. Bond overlap analyses indicated that the Hf-C bond possessed mixed covalent and ionic bond characteristics, compared with the more covalent character of the Ta-C bond. Consequently, the overall elastic properties were enhanced with increasing number of Ta-C bonds in the composites. The overall metallicity of the composites also increased with increasing TaC content; thus, the mechanical properties did not improve monotonically. Our results indicate that adding a small amount of TaC to HfC or vice versa to produce a composite would create a new UHTC with greatly improved elastic and mechanical properties as well as high-temperature thermal conductivity.