  We provide a leading order semiclassical asymptotics of the energy of bound
states for magnetic Neumann Schr\"odinger operators in two dimensional
(exterior) domains with smooth boundaries. The asymptotics is valid all the way
up to the bottom of the essential spectrum. When the spectral parameter is
varied near the value where bound states become allowed in the interior of the
domain, we show that the energy has a boundary and a bulk component. The
estimates rely on coherent states, in particular on the construction of
`boundary coherent states', and magnetic Lieb-Thirring estimates.
