The system comprises a clamping collar (10) suitable for being brought resiliently from its rest configuration in which its diameter is small to an expanded configuration. The system further comprises a support ring (20) suitable for being encircled by the collar, and an expander (40) suitable for co-operating with the ring firstly to hold the ring in an expanded configuration in which the collar (10) encircling the ring is also in its expanded configuration when the expander and the ring are in a first relative position, and secondly to enable the ring to contract and the clamping system to tighten under the resilient return force exerted by the collar encircling the ring when the expander and the ring are in a second relative position.