Magnetic dipole transitions in matter are known to be orders of magnitude weaker than their electric dipole counterparts. Nanophotonic and plasmonic structures have the potential of strongly enhancing the optical magnetic fields in the near field, making these nanostructures ideal candidates to control and enhance the emission of magnetic dipole transitions. Here we theoretically investigate the potential of resonant optical nanoantennas based on diabolo and on metal-insulator-metal diabolo configurations to strongly modify the magnetic dipole of emitters. We find that both configurations provide unprecedented 10<sup>2</sup>- to 10<sup>3</sup>-fold enhancement of the total and the radiative decay rates of a magnetic dipole moment. We show that these two nanoantennas have opposed effects on the quantum yield of the magnetic dipole, translating into different antenna efficiencies. Furthermore, by using a magnetic dipole moment as a theoretical optical nanosensor, we numerically mapped the behavior of the magnetic local density of states (MLDOS) in the entire plane close to the diabolo nanoantenna. We demonstrate the strong confinement and local enhancement of the MLDOS by the nanoantenna. As such, these results underscore the unique ability of optical nanoantennas to control light emission from magnetic dipoles, opening new technological avenues in the magneto-optical domain.