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The interplay between robotics and neuromechanics facilitates discoveries in both fields: nature provides roboticists with design ideas, while robotics research elucidates critical features that confer performance advantages to biological systems. Here, we explore a system particularly well suited to exploit the synergies between biology and robotics: high-speed antenna-based wall following of the American cockroach (Periplaneta americana). Our approach integrates mathematical and hardware modeling with behavioral and neurophysiological experiments. Specifically, we corroborate a prediction from a previously reported wall-following template - the simplest model that captures a behavior - that a cockroach antenna-based controller requires the rate of approach to a wall in addition to distance, e.g., in the form of a proportional-derivative (PD) controller. Neurophysiological experiments reveal that important features of the wall-following controller emerge at the earliest stages of sensory processing, namely in the antennal nerve. Furthermore, we embed the template in a robotic platform outfitted with a bio-inspired antenna. Using this system, we successfully test specific PD gains (up to a scale) fitted to the cockroach behavioral data in a "real-world" setting, lending further credence to the surprisingly simple notion that a cockroach might implement a PD controller for wall following. Finally, we embed the template in a simulated lateral-leg-spring (LLS) model using the center of pressure as the control input. Importantly, the same PD gains fitted to cockroach behavior also stabilize wall following for the LLS model.