  It is well-established that Whitham's modulation equations approximate the
dynamics of slowly varying periodic wave trains in dispersive systems. We are
interested in its validity in dissipative systems with a conservation law. The
prototype example for such a system is the generalized Ginzburg-Landau system
that arises as a universal amplitude system for the description of a
Turing-Hopf bifurcation in spatially extended pattern-forming systems with
neutrally stable long modes. In this paper we prove rigorous error estimates
between the approximation obtained through Whitham's modulation equations and
true solutions to this Ginzburg-Landau system. Our proof relies on analytic
smoothing, Cauchy-Kovalevskaya theory, energy estimates in Gevrey spaces, and a
local decomposition in Fourier space, which separates center from stable modes
and uncovers a (semi)derivative in front of the relevant nonlinear terms.
