Measurements of the ancient magnetic field intensity using a SQUID magnetometer are reported. The increased sensitivity of the SQUID permits the use of very small samples. These in turn make it possible to alter the Thellier method in a way that both shortens the measurement time and improves the accuracy. Most of the samples were pottery fragments and other forms of baked clay that had been fired in antiquity; samples from an historic lava flow were also included. For most of the samples an independent determination of the ancient field was available with which the values reported here are in adequate agreement.