  The hyperfine structure (hfs) and the g factor of a bound electron are caused
by external magnetic fields. For the hfs, the magnetic field is due to the
nuclear spin. A uniform-in-space and constant-in-time magnetic field is used to
probe the bound-electron g factor. The self-energy corrections to these effects
are more difficult to evaluate than those to the Lamb shift. Here, we describe
a numerical approach for both effects in the notoriously problematic regime of
hydrogen-like bound systems with low nuclear charge numbers. The calculation is
nonperturbative in the binding Coulomb field. Accurate numerical values for the
remainder functions are provided for 2P states and for nS states with n=1,2,3.
