A novel single-mode resonant structure which enables the rotation of the sample about two orthogonal axes is investigated in view of electron paramagnetic resonance applications. The proposed solution is based on cylindrical non-radiative resonators laterally loaded by the sample holder. The resulting structure can still operate in non-radiative regime, although no longer rotationally invariant. These theoretical predictions, based on symmetry considerations, are confirmed by means of a finite element numerical modelling. Theoretical and computational results are then substantiated by experimental investigations at millimeter wavelengths. As a result, a single-mode resonator which enables all the relevant rotations of the sample is demonstrated at millimeter wavelengths for the first time. In this resonator the intensity of the microwave field on the sample and its orientation with respect to the static magnetic field can be kept constant during the rotations. Therefore, a complete characterization of anisotropic systems is possible at the highest sensitivity, without the need of split-coil magnets. Possible applications at very high frequencies are discussed.