The paper presents new experimental measurements of the thermal conductivity of aqueous solutions of CaCl2 and MgCl2 at high pressure. The measurements were made with a parallel-plate apparatus. The temperatures covered the range from 293 K to 473 K with pressures up to 100 MPa and concentrations from 0.025 to 0.25 mass fractions of CaCl2 and MgCl2. The measurements include six isobars at pressures from 0.1 to 100 MPa with intervals of 20 MPa, ten isotherms at temperatures from 293 to 473 K with intervals of 20 K and six isopleths at concentrations from 0.025 to 0.25 mass fraction of CaCl2, MgCl2 with intervals of 0.05. The precision of the measurements was ±1.6%. The thermal conductivity obtained for CaCl2+H2O and MgCl2+H2O was compared with data from other authors, with satisfactory agreement. The viability of the technique was confirmed and the essential features of a high-precision instrument are established.