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For $\varepsilon>0$, let $u_\varepsilon:\Omega\to \mathbb R^2$ be a solutionof 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 theboundary $\partial \Omega$ does not grow faster than $\varepsilon^{-\alpha}$with $\alpha\in (0,1)$.

Global uniform estimate for the modulus of $2D$ Ginzburg-Landau vortexless solutions with asymptotically infinite boundary energy