  We present a methodology for computer assisted proofs of Shil'nikov
homoclinic intersections. It is based on geometric bounds on the invariant
manifolds using rate conditions, and on propagating the bounds by an interval
arithmetic integrator. Our method ensures uniqueness of the parameter for which
the homoclinic takes place. We apply the method for the Lorenz-84 atmospheric
circulation model, obtaining a sharp bound for the parameter, and also for
where the homoclinic intersection of the stable/unstable manifolds takes place.
