A novel method is described allowing quantitative evaluation of micromagnetic stray fields with submicron resolution. The method is three-dimensional in that it delivers the magnetic field vector at all points of a three-dimensional space about the specimen. The measuring principle is the deflection of an electron beam due to the Lorentz force. For a plane bundle of electron beams passing the surface of the measuring object the deflections of the beam trajectories are measured. This measurement is repeated several times while the object is beeing rotated a small angle about an axis normal to the plane spanned by the electron beams. From the data thus obtained the field is computed by means of a newly developed tomographic reconstruction procedure. Because of the inherent properties of a magnetic stray field this reconstruction procedure turns out to be far less costly then expected in view of ordinary tomography. Computer simulations and first experimental tests prove the applicability of the method.