Electric and magnetic optical fields carry the same amount of energy. Nevertheless, the efficiency with which matter interacts with electric optical fields is commonly accepted to be at least 4 orders of magnitude higher than with magnetic optical fields. Here, we experimentally demonstrate that properly designed photonic nanoantennas can selectively manipulate the magnetic versus electric emission of luminescent nanocrystals. In particular, we show selective enhancement of magnetic emission from trivalent europium-doped nanoparticles in the vicinity of a nanoantenna tailored to exhibit a magnetic resonance. Specifically, by controlling the spatial coupling between emitters and an individual nanoresonator located at the edge of a near-field optical scanning tip, we record with nanoscale precision local distributions of both magnetic and electric radiative local densities of states (LDOS). The map of the radiative LDOS reveals the modification of both the magnetic and electric quantum environments induced by the presence of the nanoantenna. This manipulation and enhancement of magnetic light-matter interaction by means of nanoantennas opens up new possibilities for the research fields of optoelectronics, chiral optics, nonlinear and nano-optics, spintronics, and metamaterials, among others.