In this paper, a Neural-Network- (NN) based guidance methodology is proposed for the high-precision docking of autonomous vehicles/platforms. The novelty of the overall online motion-planning methodology is its applicability to cases that do not allow for the direct proximity measurement of the vehicle's pose (position and orientation). In such instances, a guidance technique that utilizes Line-of-Sight- (LOS) based task-space sensory feedback is needed to minimize the detrimental impact of accumulated systematic motion errors. Herein, the proposed NN-based guidance methodology is implemented during the final stage of the vehicle's motion (i.e., docking). Systematic motion errors, which are accumulated after a long-range motion are reduced iteratively by executing corrective motion commands generated by the NN until the vehicle achieves its desired pose within random noise limits. The proposed guidance methodology was successfully tested via simulations for a 6-dof (degree-of-freedom) vehicle and via experiments for a 3-dof high-precision planar platform.