We analyzed models of volume conduction and magnetic field spread to account for aspects of spatial structure in electroencephalographic (EEG) and magnetoencephalographic (MEG) coherence. The head volume conduction model consisted of three confocal ellipsoids, representing three layers (brain, skull, and scalp) with different tissue conductivities, while the magnetic field model follows from the Biot-Savart law in a spherically symmetric medium. Source models were constructed based on magnetic resonance imaging data from three subjects, approximating neocortical current source distributions as dipoles oriented perpendicular to the local cortical surface. Assuming that every source is uncorrelated to every other source, coherence between sensors due to volume conduction and field-spread effects was estimated. Spatial properties of the model coherences were then compared with simultaneously recorded spontaneous EEG and MEG. In both models and experimental data, EEG and MEG coherence was elevated between closely spaced channels. At very large channel separations, the field-spread effect on MEG coherence appears smaller than the volume conduction effect on EEG coherence. In EEG coherence studies, surface Laplacian methods can be used to remove volume conduction effects. With single-coil magnetometers, MEG coherences are free of field effects only for sensor pairs separated by more than 20 cm. Model coherences resemble most high-frequency (e.g. >20 Hz) data; volume conduction and field-spread effects are independent of frequency, suggesting mostly uncorrelated sources in these bands. High-frequency EEG and MEG coherence can evidently serve as an estimate of coherence effects due to volume conduction and field effects, when source and head models are not available for individual subjects.