A computational study of the Faraday B term of magnetic circular dichroism at the coupled cluster singles and doubles level is presented for pyridine, pyrazine, pyrimidine, and phosphabenzene. Gauge-origin independence is obtained by expressing the B term as a total derivative of the one-photon dipole transition strength and using London orbitals. The high quality of the coupled cluster singles and doubles (CCSD) B terms makes these useful for the assignment of experimental spectra. Previous assignments of the experimental spectra based on the qualitative perimeter model are confirmed by the CCSD results for the three azines, while a reassignment is proposed for phosphabenzene. For non-overlapping bands, the B terms calculated at the equilibrium geometries are in good agreement with the experimental values. For overlapping bands, large deviations occur. Attributing a line width to the calculated equilibrium B terms leads to a large cancellation of positive and negative contributions. This cancellation may result in a large displacement of the band center maximum, leading to a large uncertainty in the assignments of "vertical experimental excitation energies" (pyridine). Bands may also completely vanish due to such cancellation (phosphabenzene). Explicit consideration of the cancellation yields simulated theoretical spectra that are in good agreement with experiment once the theoretical spectra are parallel displaced. A major contribution for this parallel displacement is the shift in the excitation energies due to correlation beyond CCSD, as seen when comparing vertical CCSD and CC3 equilibrium-geometry excitation energies.