  We explore the ideas of resurgence and Pad\'{e}-Borel resummation in the
Euler-Heisenberg Lagrangian of scalar quantum electrodynamics, which has
remained largely unexamined in these contexts. We thereby extend the related
seminal works in spinor quantum electrodynamics, while contrasting the
similarities and differences in the two cases. We investigate in detail the
efficacy of resurgent extrapolations starting from just a finite number of
terms in the weak-field expansions of the 1-loop and 2-loop scalar quantum
electrodynamics Euler-Heisenberg Lagrangian. While we re-derive some of the
well-known 1-loop and 2-loop contributions in representations suitable for
Pad\'{e}-Borel analyses, other contributions have been derived for the first
time. For instance, we find a closed analytic form for the one-particle
reducible contribution at 2-loop, which until recently was thought to be
unimportant. It is pointed out that there could be an interesting interplay
between the one-particle irreducible and one-particle reducible terms in the
strong-field limit. For the 1-loop contribution, the resurgent analysis may be
mapped effectively into two copies of the spinor quantum electrodynamics
weak-field expansions, differing only in their prefactors and masses. This
simple mapping is no longer true at 2-loops. The singularity structures in the
Pad\'{e}-Borel transforms at 1-loop and 2-loop are examined in some detail.
Analytic continuation to the electric field case and the generation of an
imaginary part is also studied. We compare the Pad\'{e}-Borel reconstructions
to closed analytic forms or to numerically computed values in the full theory.
It is seen that Pad\'{e}-Borel resummations based on even a small number of
terms from the weak-field expansions can accurately approximate the
strong-field behaviour.
