  We discuss the mapping of the conservative part of two-body electrodynamics
onto that of a test charged particle moving in some external electromagnetic
field, taking into account recoil effects and relativistic corrections up to
second post-Coulombian order. Unlike the results recently obtained in general
relativity, we find that in classical electrodynamics it is not possible to
implement the matching without introducing external parameters in the effective
electromagnetic field. Relaxing the assumption that the effective test particle
moves in a flat spacetime provides a feasible way out.
