Most rock magnetometers measure the bulk remanent magnetization of 1-inch cylindrical samples (centimeter scale) or even larger volumes of drill cores. High-Tc superconducting quantum interference device (SQUID) magnetometers are able to measure magnetic fields on rock surfaces at higher resolution on a millimeter scale: the fields of discrete rock-forming magnetic mineral grains or fine magnetic rock textures and structures can be observed when scanning across selected surface areas. The stability problems of a commercially available high-Tc SQUID magnetometer have largely been solved by improving the magnetic shielding and reducing the noise due to turbulent boiling of liquid nitrogen. Magnetizations as weak as 5¿10-4 A/m can now be discriminated with a resolution of 1 mm. A software package has been developed to eliminate measurement errors arising from instrumental drift. The program also calculates the downwards continuation of the field data and offers full inversion for the vertical magnetization component. A synthetic sample demonstrates the performance of the SQUID sensor and the inversion software. The potential of high-resolution magnetic imaging is shown by measuring three rock samples with very different magnetic properties. ¿ 2001 American Geophysical Union