  We numerically evaluate the Casimir interaction energy for configurations
involving two perfectly conducting eccentric cylinders and a cylinder in front
of a plane. We consider in detail several special cases. For quasi-concentric
cylinders, we analyze the convergence of a perturbative evaluation based on
sparse matrices. For concentric cylinders, we obtain analytically the
corrections to the proximity force approximation up to second order, and we
present an improved numerical procedure to evaluate the interaction energy at
very small distances. Finally, we consider the configuration of a cylinder in
front of a plane. We first show numerically that, in the appropriate limit, the
Casimir energy for this configuration can be obtained from that of two
eccentric cylinders. Then we compute the interaction energy at small distances,
and compare the numerical results with the analytic predictions for the first
order corrections to the proximity force approximation.
