For the vacuum interaction of asphere in front of a plane,both obeying conductor boundary conditions, we consider the approximation of small separation. We derive the next-to-leading order of the asymptotic expansion in the separation-to-radius ratio epsilon. This correction is of order epsilon. In opposite to the scalar cases it contains also contributions proportional to logarithms in first and second order, epsilon ln epsilon and epsilon(ln epsilon)(2). We compare this result with the available findings of numerical and experimental approaches.