The disclosure relates to a clamping apparatus for fixing in a recess of a component and for holding a workpiece carrier against the component. The clamping apparatus includes a housing for attachment to the workpiece carrier and a clamping sleeve for insertion into the recess. A clamping mandrel is at least partially disposed inside the clamping sleeve. The clamping mandrel is movable relative to the clamping sleeve between a release position and a clamp position. When the clamping sleeve is inserted into the recess and the clamping mandrel is in the clamp position, the clamping sleeve is braced within the recess by a holding force so as to be in a clamped position. When the clamping sleeve is in the clamped position, the housing is movable relative to the clamping mandrel, which permits the housing to move the workpiece carrier into contact with the component and apply a bearing force thereagainst.