A modified mutual inductance bridge incorporating a commercial phase‐lock amplifier has been used to measure low temperature bulk resistivities in the range from 1 to 10 000 n&OHgr; cm. No electrical contact is required with the spherical metal samples, so that possible heat leakage along electrical leads is eliminated, and measurements can be made below 40 mdeg Kelvin using a dilution refrigerator. The bridge circuit, capable of determining resistivity changes with a precision of better than 0.3%, is described.