  A class of curves with special conformal properties (conformal curves) is
studied on the Reissner-Nordstr\"om spacetime. It is shown that initial data
for the conformal curves can be prescribed so that the resulting congruence of
curves extends smoothly to future and past null infinity. The formation of
conjugate points on these congruences is examined. The results of this analysis
are expected to be of relevance for the discussion of the Reissner-Nordstr\"om
spacetime as a solution to the conformal field equations and for the global
numerical evaluation of static black hole spacetimes.
