  A foliation $(M,\mathcal{F})$ is said to be $2$--calibrated if it admits a
closed 2-form $\omega$ making each leaf symplectic. By using approximately
holomorphic techniques, a sequence $W_k$ of $2$--calibrated submanifolds of
codimension--$2$ can be found for $(M, \mathcal{F}, \omega)$. Our main result
says that the Lefschetz hyperplane theorem holds for the pairs $(F, F \cap
W_k)$, with $F$ any leaf of $\mathcal{F}$. This is applied to draw important
consequences on the transverse geometry of such foliations.
