In a bounded domain O ⊂ ℝ3 of class C1,1, the stationary Maxwell system with boundary conditions of perfect conductivity is considered. It is assumed that the dielectric permittivity and the magnetic permeability are given by η(x/ε) and μ(x/ε), where η and μ are symmetric bounded positive definite matrix-valued functions periodic with respect to some lattice in ℝ3. Here ε > 0 is a small parameter. It is known that, as ε > 0, the solutions of the Maxwell system weakly converge in L2(O) to the solutions of the homogenized Maxwell system with constant effective coefficients. Classical results are improved and approximations for the solutions in the L2(O)-norm with error estimates of operator type are found.