Haptic interfaces are special robots that interact with people to convey touch-related information. In addition to such a discriminative aspect, touch is also a highly emotionrelated sense. However, while a lot of effort has been spent to investigate the perceptual mechanisms of discriminative touch and to suitably replicate them through haptic systems in human robot interaction (HRI), there is still a lot of work to do in order to take into account also the emotional aspects of tactual experience (i.e., the so-called affective haptics), for a more naturalistic human-robot communication. In this paper, we report evidences on how a haptic device designed to convey caress-like stimuli can influence physiological measures related to the autonomous nervous system (ANS), which is intimately connected to evoked emotions in humans. Specifically, a discriminant role of electrodermal response and heart rate variability can be associated to two different caressing velocities, which can also be linked to two different levels of pleasantness. Finally, we discuss how the results from this study could be profitably employed and generalized to pave the path towards a novel generation of robotic devices for HRI.