A gripping device (100) for holding, centring and/or clamping a micromechanical or horological component (200) in a chamber delimited by a collet including at least one movable jaw (2) and at least one stationary jaw (3), wherein some of the movable jaws (2) and/or stationary jaws (3) include a reference surface (20) to support a component (200) bearing frontally thereagainst, and the gripping device (100) includes both, on the one hand, stationary jaws (3) including the reference surface (20) to support the component (200) bearing thereagainst, and movable jaws (2) for centring and/or clamping the component (200), and on the other hand a vacuum generator (60) for creating the vacuum in the clamping chamber. Also a related method.