The elliptic problem - div ⁡ ( μ ⁢ ∇ ⁡ u ) = f -\operatorname{div}(\mu\nabla u)=f is considered, where μ > 0 \mu>0 is smooth but strongly varying. Anisotropic a posteriori error estimates are derived, the effectivity index being bounded above and below by two constants independent of the data 𝑓, 𝜇, the mesh size and aspect ratio, up to higher order terms. Numerical experiments on non-adapted and adapted anisotropic meshes confirm these predictions.