During strong earthquakes, structural pounding may occur between structures (buildings, bridges, strategic facilities, critical equipment, etc.) and the surrounding moat wall because of the limited separation distance and the deformations of the isolator. An arrangement that favors the solution of this problem is the interposition of shock absorbers. Thus, the influence of geometrical and mechanical characteristics of isolation and mitigation devices on nonlinear, nonsmooth response of vibro-impact systems is experimentally investigated in this paper on the basis of a laboratory campaign of experimental tests. Shaking table tests were carried out under a harmonic excitation in order to investigate two different configurations: the absence and the presence of bumpers. Three different values of the table acceleration peak were applied, four different amplitude values of the total gap between mass and bumpers were considered, and also four different types of bumpers were employed; moreover, two problems were addressed, namely, control of excessive displacements and control of excessive accelerations, and hence, two types of normalization were adopted in order to better interpret experimental results. Suitable choices of pairs of bumpers and gaps were suggested as a trade-off between conflicting objectives. Furthermore, a numerical model was proposed, and its governing parameters identified in order to simulate the experimental results.