The suspension systems generally installed in road racing motorcycles make it possible to fine tune the damping characteristics through a wide range of adjustments, so that the amount of force delivered for low and high suspension shaft speed, in both compression and rebound states, can be independently set by the user. Nevertheless, the optimal choice of suspension tuning parameters is a difficult task, normally affecting the vehicle dynamic behavior and its handling characteristics, and technical literature lacks procedures being developed and adopted in practice for this purpose. In this paper a handling-oriented algorithm for the optimization of the suspension damping parameters of a passively suspended racing motorcycle is presented. An optimization function is proposed for two significant maneuvers in road racing, such as high lean angle cornering and braking. The related objective functions are based on the minimization of the fluctuating component of the vertical front tire-ground force, allowing the tire to maximize the friction contact actions, that is maximizing the vehicle's ability to accelerate. The above maneuvers are simulated by means of a multibody motorcycle model where the suspensions non-linearity is taken into account. The experimental damping force versus suspension shaft speed relationship is modeled by means of a non-parametric B-spline piecewise function, whose coefficients are determined by a mixed interpolation-approximation procedure, and their choice and values are restrained by manufacturability constraints. This makes it possible to properly model the effects of the tuning control parameters and of the dry friction with a minimum number of parameters. Moreover, it is shown that a computationally efficient optimization can be performed using this properly designed B-spline coefficients as optimization variables.