The design of many promising, newly emerging classes of photonic metamaterials and subwavelength confinement structures requires detailed knowledge and understanding of the electromagnetic near-field interactions between their building blocks. While the electric field distributions and, respectively, the electric interactions of different nanostructures can be routinely measured, for example, by scattering near-field microscopy, only recently experimental methods for imaging the magnetic field distributions became available. In this paper, we provide direct experimental maps of the lateral magnetic near-field distributions of variously shaped plasmonic nanoantennas by using hollow-pyramid aperture scanning near-field optical microscopy (SNOM). We study both simple plasmonic nanoresonators, such as bars, disks, rings and more complex antennas. For the studied structures, the magnetic near-field distributions of the complex resonators have been found to be a superposition of the magnetic near-fields of the individual constituting elements. These experimental results, explained and validated by numerical simulations, open new possibilities for engineering and characterization of complex plasmonic antennas with increased functionality.