Autocollimators are versatile devices for the contactless measurement of the tilt angles of reflecting surfaces. In their practical application, e.g., in deflectometric profilometers for the precision form measurement of optical surfaces, the autocollimator beam is deflected in two orthogonal angular directions simultaneously. The concurrent engagement of both measuring axes results in errors in their angle response due to the crosstalk between them, which need to be calibrated. In this contribution, the capabilities of autocollimator calibration at the Physikalisch-Technische Bundesanstalt (PTB) are presented. The measurement of spatial angles is discussed in detail with a focus on achieving traceability of this measurand and reaching lowest uncertainties. A novel concept is introduced, which makes use of an innovative Cartesian arrangement of three autocollimators (two reference autocollimators and the autocollimator to be calibrated) facing a reflector cube. Each of the two reference autocollimators, which are used for the precise measurement of the cube’s angular orientation, is primarily sensitive to rotations of the cube around one of the two relevant axes and can, thus, be calibrated and traced back to PTB’s national primary standard for the plane angle in a conventional manner. In this way, the measurement of spatial angles is effectively divided into two separate measurements of plane angles. The mechanical realisation of the setup at PTB is described.