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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.