Plasmonic nanoparticles are commonly used to tune and direct the radiation from electric dipolar emitters. Less progress has been made towards understanding complementary systems of magnetic nature. However, it has been recently shown that high-index dielectric spheres can act as effective magnetic antennas. Here we explore the concept of coupling dielectric magnetic antennas with either an electric or magnetic dipolar emitter in a similar fashion to the purely electric systems reported previously. We investigate the enhancement of radiation from systems comprising admixtures of these electric and magnetic elements and perform a full study of its dependence on the distance and polarization of the emitter with respect to the antenna. A comparison to the plasmon antennas reveals remarkable symmetries between electric and magnetic systems, which might lead to novel paradigms in the design of nanophotonic devices that involve magnetic activity.