Augmented reality (AR) Head-Mounted Displays (HMDs) are emerging as the most efficient output medium to support manual tasks performed under direct vision. Despite that, technological and human-factor limitations still hinder their routine use for aiding high-precision manual tasks in the peripersonal space. To overcome such limitations, in this work, we show the results of a user study aimed to validate qualitatively and quantitatively a recently developed AR platform specifically conceived for guiding complex 3D trajectory tracing tasks. The AR platform comprises a new-concept AR video see-through (VST) HMD and a dedicated software framework for the effective deployment of the AR application. In the experiments, the subjects were asked to perform 3D trajectory tracing tasks on 3D-printed replica of planar structures or more elaborated bony anatomies. The accuracy of the trajectories traced by the subjects was evaluated by using templates designed ad hoc to match the surface of the phantoms. The quantitative results suggest that the AR platform could be used to guide high-precision tasks: on average more than 94% of the traced trajectories stayed within an error margin lower than 1 mm. The results confirm that the proposed AR platform will boost the profitable adoption of AR HMDs to guide high precision manual tasks in the peripersonal space.