Magnetic field maps can rapidly and accurately be acquired on the surface of a cylinder or sphere with an array of nuclear magnetic resonance (NMR) coils multiplexed to a single radiofrequency receiver. Using an array of NMR probes significantly decreases the time necessary to map B0 and improves field map accuracy because the probes do not move. The spatial variation of the Larmor frequency is used to determine the spherical harmonic components present in the field. A limitation of this approach is that NMR resonant circuits are inherently narrow band which limits the apparatus to a specific field strength and only points in space defined by the array layout. This apparatus can characterize the magnetic fields of high homogeneity dipole magnets, quadrupole magnets, gradient coils, and shims used in NMR imaging systems.