A clamping device 20 for clamping to an implant 1 (e.g. an acetabular cup 2) comprises a base component 21 having a first edge 22 engageable with the implant and a clamping component 24 having engaging means 25 engageable with the implant at a distance beyond the first edge so as to define an island of implant material 26 there-between. A sliding interface 27 between the two components is capable of causing a pulling force to pull the engaging means towards the first edge upon application of an actuating force (for example by tightening of screw 23) on the clamping component, gripping the said island of material between the base component and clamping component. An implant for use with the device has a groove 7 on its outer surface with which the first component can engage and a continuous notch 8 on its top surface with which the engaging means can engage, the island of material 26 being defined between the groove and notch.