  We prove a quantitative convergence result of the nonlocal Allen--Cahn
equation to volume-preserving mean curvature flow. The proof uses gradient flow
calibrations and the relative entropy method, which has been used in the recent
literature to prove weak-strong uniqueness results for mean curvature flow and
convergence of the Allen--Cahn equation. A crucial difference in this work is a
new notion of gradient flow calibrations. We add a tangential component to the
velocity field in order to prove the Gronwall estimate for the relative energy.
This allows us to derive the optimal convergence rate without having to show
the closeness of the Lagrange-multipliers.
