  The semiclassical magnetic Neumann Schr\"odinger operator on a smooth,
bounded, and simply connected domain $\Omega$ of the Euclidean plane is
considered. When $\Omega$ has a symmetry axis, the semiclassical splitting of
the first two eigenvalues is analyzed. The first explicit tunneling formula in
a pure magnetic field is established. The analysis is based on a
pseudo-differential reduction to the boundary and the proof of the first known
optimal purely magnetic Agmon estimates.
