  We show that roughness or surface modulations change the distance dependence
of (power-law) interactions between curved objects at proximity. The modified
scaling law is then simply related to the order of the first non-vanishing
coefficient of the Taylor expansion of the distribution of separations between
the surfaces. The latter can in principle be estimated by scanning
measurements, or computed for well characterized modulations, and then used to
predict short-distance scaling behavior in disparate experiments. For example,
we predict that the radiative heat transfer between a rough sphere and a plate
approaches a constant with decreasing separation. Similar saturation is
expected for the Casimir force between dielectric or metallic surfaces with
appropriate modulations over distinct length scales.
