  Pair-production of magnetic Reissner-Nordstr\"{o}m black holes (of charges
$\pm q$) was recently studied in the leading WKB approximation. Here, we
consider generic quantum fluctuations in the corresponding instanton geometry
given by the Euclidean Ernst metric, in order to simulate the behaviour of the
one-loop tunneling rate. A detailed study of the Ernst metric suggests that for
sufficiently weak field $B$, the problem can be reduced to that of quantum
fluctuations around a single near-extremal Euclidean black hole in thermal
equilibrium with a heat bath of finite size. After appropriate renormalization
procedures, typical one-loop contributions to the WKB exponent are shown to be
inversely proportional to $B$, as $B\rightarrow 0$, indicating that the leading
Schwinger term is corrected by a small fraction $\sim \hbar /q^2$. We
demonstrate that this correction to the Schwinger term is actually due to a
semiclassical shift of the black hole mass-to-charge ratio that persists even
in the extremal limit. Finally we discuss a few loose ends.
