The electrical conductivity of Na, Mg-bearing carbonate melts was measured in a Kawai-type multi-anvil apparatus as a function of pressure. The carbonate samples were mixtures of MgCO3 and Na2CO3 or Mg5(CO3)4(OH)2·4(H2O) and Na2CO3. High-pressure experiments on the carbonate systems were performed up to 1800 K in a wide pressure range from 3.4 to 10.9 GPa. The sample conductivity abruptly changed at the eutectic temperature, which increased with increasing pressure. The hydrous carbonate yielded a lower eutectic temperature than the anhydrous carbonate and showed weaker pressure dependence. The molten state carbonates showed very high electrical conductivity with temperature dependence following the Arrhenius law. As the pressure increased, the conductivity decreased. The negative pressure dependence of the electrical conductivity of the hydrous carbonate melt was larger than that of the anhydrous one. The activation volumes were ΔV = 1.81 and 3.61 cm mol−1 for the anhydrous and hydrous carbonate melts, respectively. The high electrical conductivity observed in the mantle beneath the Slave and Brazilian cratons can be explained by the process of lithospheric rejuvenation due to a small amount of hydrous carbonated melt released from the crystallization of the kimberlitic magma at the base of the continental mantle lithosphere.