An apparatus for measuring objects, in particular to a coordinate measuring unit, is provided. The unit has a probe which is movable relative to an object to be measured by means of an actuator to sample the surface of the object in a contacting manner, wherein a sampling body, whose front end is designed as a measuring tip for a contact with the object is supported at the probe. The relative position of the measuring tip with respect to the probe is determined. The sampling body is supported at the probe with movement play along at least one direction. A change in the inclination of the sampling body relative to the probe, or vice versa, can be detected via a measurement of a test parameter.