  We compute the sum and number of eigenvalues for a certain class of magnetic
Schrodinger operators in a domain with boundary. Functions in the domain of the
operator satisfy a (magnetic) Robin condition. The calculations are valid in
the semi-classical asymptotic limit and the eigenvalues concerned correspond to
eigenstates localized near the boundary of the domain. The formulas we derive
display the influence of the boundary and the boundary condition and are valid
under a weak regularity assumption of the boundary function. Our approach
relies on three main points: reduction to the boundary; construction of
boundary coherent states; handling the boundary term as a surface electric
potential and controlling the errors by various Lieb-Thirring inequalities.
