Service robots have the potential to support the personal mobility of elderly population. Monitoring and measuring grasping force in older adults is an important issue both from robotic and clinical perspectives. From robot point of view, new adaptive control strategies can be implemented based on the users' force; clinicians can monitor the changes in the grasp strength over time to evaluate abnormal conditions, which can be associated with geriatric syndromes. In this context, this work focused on the design, development and testing of a sensorized smart handle able to enhance the robotic mobility support service provided by the robot, called ASTRO. The primary goal of this paper is to design the sensorized handle according to clinical and technical specifications in terms of working range, sensitivity and clinical requirements. Then, the smart handle was tested with 19 subjects to investigate whether the system is able to detect forces correlated to the ones measured with a traditional tool. Additionally, further analysis were conducted to analyse how the forces were distributed to refine and optimize the design. The study shows meaningful results as the grasp forces measured with the smart handle and the traditional tool were significantly correlated.