The invention relates to checking or calibrating the angle-dependent alignment of a reference structure on a high-precision test-piece. A device comprises a plinth, and a retainer piece, rotatably mounted about a retainer piece axis, for retaining the test-piece and a measuring piece with a measuring piece bearing unit, to rotationally mount the measuring piece, about a measuring piece axis. An optical unit is mounted on the measuring piece, for receiving at least one test-piece beam, interacting with the reference structure on the test piece, running essentially in a measuring plane. The measuring piece bearing unit is arranged on the measuring plane or to one side thereof. The measuring piece includes a base that is, for example, axially symmetrical with the measuring piece axis encompassing or surrounding the intersection of the measuring piece axis with the retainer piece axis and hence also encompasses or surrounds the test-piece.