  For $\varepsilon>0$, let $u_\varepsilon:\Omega\to \mathbb R^2$ be a solution
of the Ginzburg-Landau system $$-\Delta u_\varepsilon=\frac 1{\varepsilon^2}
u_\varepsilon (1-|u_\varepsilon|^2)$$ in a Lipschitz bounded domain $\Omega$.
In an energy regime that excludes interior vortices, we prove that
$1-|u_\varepsilon|$ is uniformly estimated by a positive power of $\varepsilon$
$globally$ in $\Omega$ provided that the energy of $u_\varepsilon$ at the
boundary $\partial \Omega$ does not grow faster than $\varepsilon^{-\alpha}$
with $\alpha\in (0,1)$.
