  In this paper we study local stability estimates for a magnetic Schr\"odinger
operator with partial data on an open bounded set in dimension $n\geq 3$. This
is the corresponding stability estimates for the identifiability result
obtained by Bukgheim and Uhlmann $[2]$ in the presence of magnetic field and
when the measurements for the Dirichlet-Neumann map are taken on a neighborhood
of the illuminated region of the boundary for functions supported on a
neighborhood of the shadow region. We obtain $\log$-type estimates.
