Clamp (1) for holding a container (2) by a neck (3) in a container handling machine (5), said clamp comprising a body (7) for mounting the clamp (1) on a rotary support (4), and a pair of resilient arms (11) protruding sidewise from the body (7) and each provided with a gripping jaw (12), wherein each resilient arm (11) comprises: an inner section (13) extending along the body (7) and connected thereto at a first back end junction (16); an intermediate section (14) extending substantially parallel to the inner section (13) and connected thereto at a front end junction (17); an outer section (15), provided, at a front end, with a gripping jaw (12), and extending substantially parallel to the intermediate section (14) and connected thereto at a second back end junction (18).