The formalism in order to obtain the Dark Energy equation of state is extended to non-flat universes and we consider the inequalities that must be satisfied by Phantom Dark Energy in this case . We show that due to a non-vanishing spatial curvature satisfying the observational bounds , the uncertainty on the determination of the Dark Energy equation of state parameter w , when it is taken constant , can be significant and that it is minimal for some redshift z _ { cr } \sim 3 . We consider the potential of future measurements of the gravitational waves emitted by binaries at high redshifts z > z _ { cr } to reduce this uncertainty . Results obtained here should also be relevant for a weakly varying equation of state with w \approx - 1 .