This article presents a system for soft human–robot handshaking, using a soft robot hand in conjunction with a lightweight and impedance-controlled robot arm. Using this system, we study how different factors influence the perceived naturalness, and give the robot different personality traits. Capitalizing on recent findings regarding handshake grasp force regulation, and on studies of the impedance control of the human arm, we investigate the role of arm stiffness as well as the kinesthetic synchronization of human and robot arm motions during the handshake. The system is implemented using a lightweight anthropomorphic arm, with a Pisa/IIT Softhand wearing a sensorized silicone glove as the end-effector. The robotic arm is impedance-controlled, and its stiffness changes according to different laws under investigation. An internal observer is employed to synchronize the human and robot arm motions. Thus, we simulate both active and passive behavior of the robotic arm during the interaction. Using the system, studies are conducted where 20 participants are asked to interact with the robot, and then rate the perceived quality of the interaction using Likert scales. Our results show that the control of the robotic arm kinesthetic behavior does have an effect on the interaction with the robot, in term of its perceived personality traits, responsiveness, and human-likeness. Our results pave the way towards robotic systems that are capable of performing human–robot interactions in a more human-like manner, and with personality.