  The discovery of very-high-energy (VHE, E > 100 GeV) gamma-ray emission from
intermediate- and low-frequency peaked blazars suggests that gamma-gamma
absorption and pair cascading might occur in those objects. In previous papers,
we investigated the Compton emission from VHE gamma-ray induced pair cascades,
deflected by moderate magnetic fields, in a largely model-independent way, and
demonstrated that this emission can explain the Fermi fluxes and spectra of the
radio galaxies Cen A and NGC 1275. In this paper, we describe a generalization
of our Monte-Carlo cascade code to include the angle-dependent synchrotron
output from the cascades, allowing for the application to situations with
non-negligible magnetic fields, leading to potentially observable synchrotron
signatures, but still not dominating the radiative energy loss of cascade
particles. We confirm that the synchrotron radiation from the cascades in NGC
1275 and Cen A are negligible for the parameters used in our previous works. We
demonstrate that the magnetic field can not be determined from a fit of the
cascade emission to the gamma-ray spectrum alone, and the degeneracy can only
be lifted if the synchrotron emission from the cascades is observed as well. We
illustrate this fact with the example of NGC 1275. We point out that the
cascade synchrotron emission may produce spectral features in the same energy
range in which the big blue bump is observed in the spectral energy
distributions of several blazars, and may make a non-negligible contribution to
this feature. We illustrate this idea with the example of 3C 279.
