  We investigate the $\mathrm{Pin}^-(2)$-monopole invariants of symplectic
$4$-manifolds and K\"{a}hler surfaces with real structures. We prove the
nonvanishing theorem for real symplectic $4$-manifolds which is an analogue of
Taubes' nonvanishing theorem of the Seiberg-Witten invariants for symplectic
$4$-manifolds. Furthermore, the Kobayashi-Hitchin type correspondence for real
K\"{a}hler surfaces is given.
