  In this article we consider an inverse boundary value problem for the
time-harmonic Maxwell equations. We show that the electromagnetic material
parameters are determined by boundary measurements where part of the boundary
data is measured on a possibly very small set. This is an extension of earlier
scalar results of Bukhgeim-Uhlmann and Kenig-Sj\"ostrand-Uhlmann to the Maxwell
system. The main contribution is to show that the Carleman estimate approach to
scalar partial data inverse problems introduced in those works can be carried
over to the Maxwell system.
