  In this paper, we show that the oriented diameter of any $n$-vertex
$2$-connected near triangulation is at most $\lceil{\frac{n}{2}}\rceil$ (except
for seven small exceptions), and the upper bound is tight. This extends a
result of Wang et.al. on the oriented diameter of maximal outerplanar graphs,
and improves an upper bound of $n/2+O(\sqrt{n})$ on the oriented diameter of
planar triangulations by Mondal, Parthiban and Rajasingh.
