We consider the following singularly perturbed reaction-diffusion equationwith a small parameter € > 0 and double obstacle potential ψ. The zero level set ofapproximates the evolution of a surfaceof codimension 1, which moves in its inner normal direction with velocityThis approach is insensitive to the choice of the potential ψ and thus differs from the usual Allen-Cahn approximation. We prove optimal interface error estimates of order O(€2), for smooth flows. To this aim we construct proper barriers dictated by formal asymptotics, we introduce a modified distance function, and we exploit the validity of a comparison lemma. Finally we present some numerical results.