A meandering winding magnetometer (MWM) includes a meandering primary winding and at least one sensing winding or coil on a membrane to be pressed against a test surface. The membrane may be supported on a flexible carrier which is translatable into a probe. Abutments in the probe press the carrier against the test surface but allow the carrier and membrane to conform to the test surface. One MWM circuit includes meandering primary and secondary windings. The return leads from the secondary winding return to connector pads in close alignment with the test array, while leads from the primary winding are spaced at least one wavelength from the array. In another MWM circuit, individual sensing loops are positioned within the meandering primary winding. The MWM circuit may be provided on an adhesive tape which may be cut to length.