For the analysis of the angular dependence of electron paramagnetic resonance (EPR) spectra of low-symmetry centres with S = 1/2 in three independent planes, it is well-established—but often overlooked—that an ambiguity may arise in the best-fit tensor result. We investigate here whether a corresponding ambiguity also arises when determining the hyperfine coupling (HFC) tensor for nuclei with I = 1/2 from angular dependent electron nuclear double resonance (ENDOR) measurements. It is shown via a perturbation treatment that for each set of MS ENDOR branches two best-fit tensors can be derived, but in general only one unique solution simultaneously fits both. The ambiguity thus only arises when experimental data of only one MS multiplet are used in analysis or in certain limiting cases. It is important to realise that the ambiguity occurs in the ENDOR frequencies and therefore the other best-fit result for an ENDOR determined tensor depends on various details of the ENDOR experiment: the MS state of the fitted transitions, the microwave frequency (or static magnetic field) in the ENDOR measurements and the rotation planes in which data have been collected. The results are of particular importance in the identification of radicals based on comparison of theoretical predictions of HFCs with published literature data. A procedure for obtaining the other best-fit result for an ENDOR determined tensor is outlined.