  In a bounded domain $\mathcal{O}\subset\mathbb{R}^3$ of class $C^{1,1}$, we
consider a stationary Maxwell system with the perfect conductivity boundary
conditions. It is assumed that the dielectric permittivity and the magnetic
permeability are given by $\eta({\mathbf x}/ \varepsilon )$ and $\mu({\mathbf
x}/ \varepsilon )$, where $\eta( {\mathbf x})$ and $\mu({\mathbf x})$ are
symmetric $(3 \times 3)$-matrix-valued functions; they are periodic with
respect to some lattice, bounded and positive definite. Here $\varepsilon >0$
is the small parameter. We use the following notation for the solutions of the
Maxwell system: ${\mathbf u}_\varepsilon$ is the electric field intensity,
${\mathbf v}_\varepsilon$ is the magnetic field intensity, ${\mathbf
w}_\varepsilon$ is the electric displacement vector, and ${\mathbf
z}_\varepsilon$ is the magnetic displacement vector. It is known that ${\mathbf
u}_\varepsilon$, ${\mathbf v}_\varepsilon$, ${\mathbf w}_\varepsilon$, and
${\mathbf z}_\varepsilon$ weakly converge in $L_2({\mathcal O})$ to the
corresponding homogenized fields ${\mathbf u}_0$, ${\mathbf v}_0$, ${\mathbf
w}_0$, and ${\mathbf z}_0$ (the solutions of the homogenized Maxwell system
with the effective coefficients), as $\varepsilon \to 0$. We improve the
classical results and find approximations for ${\mathbf u}_\varepsilon$,
${\mathbf v}_\varepsilon$, ${\mathbf w}_\varepsilon$, and ${\mathbf
z}_\varepsilon$ in the $L_2({\mathcal O})$-norm. The error terms do not exceed
$C \sqrt{\varepsilon} (\| {\mathbf q}\|_{L_2}+\|{\mathbf r}\|_{L_2})$, where
the divergence free vector-valued functions ${\mathbf q}$ and ${\mathbf r}$ are
the right-hand sides of the Maxwell equations.
