Successful exploration for subsurface water on Mars is critical to future scientific endeavors on the planet. Although many sophisticated systems have been proposed for directly detecting water on Mars, it is worthwhile to look at the methods that are used in practice for water exploration in basaltic terrain on Earth. By far, the most commonly used instrument for this purpose, at least in the initial stages of exploration, is the magnetometer. The purpose of doing reconnaissance and detailed magnetic surveys for water exploration is not for direct detection but to find those subsurface geological environments in which water is most likely to reside. Magnetic surveys in the basalt-covered Columbia Plateau are commonly used for such diverse tasks as locating buried valleys, delineating hidden faults, mapping contacts, and tracing dikes. This information leads to the discovery of groundwater, not directly but indirectly. On Mars, just as it is on Earth, the ultimate water supply problem will be a local one: exactly where to drill for water. The unpretentious magnetometer will prove to be a most useful geophysical instrument for making that decision. An important side benefit of using low-altitude magnetic field measurements for groundwater exploration on Mars is the insight such near-surface measurements will provide on the nature of the planet's ancient magnetic field.