  We consider the computation of averaged coefficients for the homogenization
of elliptic partial differential equations. In this problem, like in many
multiscale problems, a large number of similar computations parametrized by the
macroscopic scale is required at the microscopic scale. This is a framework
very much adapted to model order reduction attempts. The purpose of this work
is to show how the reduced-basis approach allows to speed up the computation of
a large number of cell problems without any loss of precision. The essential
components of this reduced-basis approach are the {\it a posteriori} error
estimation, which provides sharp error bounds for the outputs of interest, and
an approximation process divided into offline and online stages, which
decouples the generation of the approximation space and its use for Galerkin
projections.
