This paper presents a novel electromyography (EMG)-driven hand exoskeleton for bilateral rehabilitation of grasping in stroke. The developed hand exoskeleton was designed with two distinctive features: (a) kinematics with intrinsic adaptability to patient's hand size, and (b) free-palm and free-fingertip design, preserving the residual sensory perceptual capability of touch during assistance in grasping of real objects. In the envisaged bilateral training strategy, the patient's non paretic hand acted as guidance for the paretic hand in grasping tasks. Grasping force exerted by the non paretic hand was estimated in real-time from EMG signals, and then replicated as robotic assistance for the paretic hand by means of the hand-exoskeleton. Estimation of the grasping force through EMG allowed to perform rehabilitation exercises with any, non sensorized, graspable objects. This paper presents the system design, development, and experimental evaluation. Experiments were performed within a group of six healthy subjects and two chronic stroke patients, executing robotic-assisted grasping tasks. Results related to performance in estimation and modulation of the robotic assistance, and to the outcomes of the pilot rehabilitation sessions with stroke patients, positively support validity of the proposed approach for application in stroke rehabilitation.