At CERN, magnetic measurement activities typically concern fields up to about 10 T, with uncertainties in the 10-100 ppm range. In some cases, however, measurement and control of very low fields, in the range of nano to microcrotesla, is needed. In this talk, we shall first review briefly such cases, which are mostly motivated by the mitigation of beam perturbations at very low energy or over large regions. Next we will discuss the instrumentation best suited for such low levels, including both custom-made and commercially available sensors, which are mostly designed for geomagnetic applications. Finally, we will list the specific capabilities available at CERN in this area, which include commercial teslameters of various types, manufacturing capabilities for inductive sensors, controllable scalar and vector field sources and other test and calibration facilities.