The spatial distribution of electromagnetic fields emitted from the aperture tip of a scanning near-field optical microscope (SNOM), which is called the emission pattern, depends on the geometry of the apex and the material composition of the tip’s coating. In previous works, experimental measurements of the emission pattern from the aperture tip were performed mostly in the far field. Moreover, the corresponding theoretical models were also developed based on these far-field measurements. Here, we have used the automated dual-tip SNOM to systematically characterize the emission from the aperture tip in the near field. In this regard, we have considered three different pairs of excitation and detection tips with distinct geometries. The emission patterns of the excitation tips were mapped using detection tips. Unidirectional surface plasmon polaritons (SPPs) at the surface of a gold platelet were launched by an excitation tip and measured in the near field by the detection tip. The experimental results were numerically reproduced by means of the Bethe–Bouwkamp model. This work puts into evidence the applicability of the automated dual-tip SNOM as the only available characterization technique to measure the emission from aperture tips in the near field. The reported asymmetric SPP radiation patterns can find applications in photonic integrated circuits or in biological and chemical sensing.