A man–machine teleoperation system for a continuum robot tailored to endovascular interventions and based on a leader–follower architecture is presented. The leader robotic catheter is manually shaped by the surgeon and equipped with distributed fiber-optic shape sensors. The follower catheter inserted into the patient’s vasculature is tracked exclusively by computer-vision algorithms and instrumented with force sensors. Inverse-kinematics algorithms reproduce the leader configuration on the follower, while a closed-loop sensory channel conveys contact forces to the operator as adjustable mechanical resistance, creating a tangible sense of presence. The system fulfils the core principles of collaborative robotics-intuitive manipulation, bidirectional feedback, adaptive motion constraints, and patient safety. Potential extensions include learning from demonstration and predictive control. The proposed system can serve as a foundation for next-generation robotic platforms enabling minimum invasive procedures under limited visual feedback.