Methods and apparatus for determining the orientation and the position of an object in space with the assistance of a sensing instrument are provided. The sensing instrument is provided with a marking element. The orientation and position of the marking element is determinable by means of the navigation system. In order to be able to carry out a reliable determination of the position, even under confined conditions of access, the sensing instrument is adapted to be successively connected in a guided manner to the object for free rotation about two non-parallel, defined axes of rotation. The sensing instrument can be rotated about these axes of rotation, and the orientation and the position of the two defined axes of rotation in space and hence the orientation and the position of the object in space can be calculated from the resulting movement of the marking element during this rotation.