  Consider analytic generic unfoldings of the three dimensional conservative
Hopf-Zero singularity. Under open conditions on the parameters determining the
singularity, the unfolding possesses two saddle-foci when the unfolding
parameter is small enough. One of them has one dimensional stable manifold and
two dimensional unstable manifold whereas the other one has one dimensional
unstable manifold and two dimensional stable manifold. Baldom\'a, Castej\'on
and Seara [BCS13] gave an asymptotic formula for the distance between the one
dimensional invariant manifolds in a suitable transverse section. This distance
is exponentially small with respect to the perturbative parameter, and it
depends on what is usually called a Stokes constant. The non-vanishing of this
constant implies that the distance between the invariant manifolds at the
section is not zero. However, up to now there do not exist analytic techniques
to check that condition. In this paper we provide a method for obtaining
accurate rigorous computer assisted bounds for the Stokes constant. We apply it
to two concrete unfoldings of the Hopf-Zero singularity, obtaining a computer
assisted proof that the constant is non-zero.
