Where should a magnetic field be measured?

We argue that the answer to the above question is: on the boundary of the volume in which the field is to be known. We assume that in this volume the field is divergence- and rotational-free, that the measurements have an error which is random and uncorrelated, and that only these errors limit the accurate description of the field. In a practical case it is shown that observations inside the volume can indeed be predicted accurately from measurements on the boundary. The time and effort involved in the measurement can thus be substantially reduced.