Given a closed Riemann surface $R$ of genus $p \geq 2$ together
with an anticonformal involution $\tau:R \to R$ with fixed points,
we consider the group $K(R,\tau)$ consisting of the conformal and
anticonformal automorphisms of $R$ which commute with $\tau$. It
is a well known fact due to C. L. May that the order of
$K(R,\tau)$ is at most $24(p-1)$ and that such an upper bound is
attained for infinitely many, but not all, values of $p$. May also
proved that for every genus $p \geq 2$ there are surfaces for
which the order of $K(R,\tau)$ can be chosen to be $8p$ and
$8(p+1)$. These type of surfaces are called \textit{May surfaces}.
In this note we construct real Schottky uniformizations of every
May surface. In particular, the corresponding group $K(R,\tau)$
lifts to such an uniformization. With the help of these real
Schottky uniformizations, we obtain (extended) symplectic
representations of the groups $K(R,\tau)$. We study the families
of principally polarized abelian varieties admitting the given
group of automorphisms and compute the corresponding Riemann
matrices, including those for the Jacobians of May surfaces.