  In this article, we study stability estimates when recovering magnetic fields
and electric potentials in a simply connected open subset in $R^n$ with $n \geq
3$, from measurements on open subsets of its boundary. This inverse problem is
associated with a magnetic Schr\"odinger operator. Our estimates are
quantitative versions of the uniqueness results obtained by D. Dos Santos
Ferreira, C. E. Kenig, J. Sj\"ostrand and G. Uhlmann in [13]. The moduli of
continuity are of logarithmic type.
