In some applications it is useful to consider variants of H-measures different from those introduced in the classical or the parabolic case. We introduce the notion of admissible manifold and define variant H-measures on $R^d \times P$ for any admissible manifold P. In the sequel we study one special variant, fractional H-measures with orthogonality property, where the corresponding manifold and projection curves are orthogonal, as it was the case with classical or parabolic H-measures, and prove the localisation principle. Finally, we present a simple application of the localisation principle.