  In this paper, we determine the convergence speed of an upscaling of a
pseudo-parabolic system containing drift terms with scale separation of size
$\epsilon \ll 1$. Both the upscaling and convergence speed determination
exploit a natural spatial-temporal decomposition, which splits the
pseudo-parabolic system into a spatial elliptic partial differential equation
and a temporal ordinary differential equation. We extend the applicability to
space-time domains that are a product of spatial and temporal domains, such as
a time-independent perforated spatial domain. Finally, for special cases we
show convergence speeds for global times, i.e. $t \in \mathbf{R}_+$, by using
time intervals that converge to $\mathbf{R}_+$ as $\epsilon\downarrow 0$.
