Surgical methods and devices allow closed-chest surgery to be performed on a heart of a patient while the heart is beating. A region of the heart is stabilized by engaging a surface of the heart with a stabilizer without having to stop the heart. Motion of the target tissues is inhibited sufficiently to treat the target tissues with robotic surgical tools which move in response to inputs of a robotic system operator. A stabilizing surface of the stabilizer is coupled to a drive system to position the surface from outside the patient, preferably by actuators of the robotic servomechanism. Exemplary stabilizers includes a suture or other flexible tension member spanning between a pair of jointed bodies, allowing the member to occlude a coronary blood vessel and/or help stabilize the target region between the stabilizing surfaces.