  The mirror of a projective toric manifold $X_\Sigma$ is given by a
Landau-Ginzburg model $(Y,W)$. We introduce a class of Lagrangian submanifolds
in $(Y,W)$ and show that, under the SYZ mirror transformation, they can be
transformed to torus-invariant hermitian metrics on holomorphic line bundles
over $X_\Sigma$. Through this geometric correspondence, we also identify the
mirrors of Hermitian-Einstein metrics, which are given by distinguished
Lagrangian sections whose potentials satisfy certain Laplace-type equations.
