  In the current drive to quantum-simulate evermore complex gauge-theory
phenomena, it is necessary to devise schemes allowing for the control and
suppression of unavoidable gauge-breaking errors on different experimental
platforms. Although there have been several successful approaches to tackle
coherent errors, comparatively little has been done in the way of decoherence.
By numerically solving the corresponding Bloch--Redfield equations, we show
that the recently developed method of \textit{linear gauge protection}
suppresses the growth of gauge violations due to $1/f^\beta$ noise as
$1/V^\beta$, where $V$ is the protection strength and $\beta>0$, in Abelian
lattice gauge theories, as we show through exemplary results for
$\mathrm{U}(1)$ quantum link models and $\mathbb{Z}_2$ lattice gauge theories.
We support our numerical findings with analytic derivations through
time-dependent perturbation theory. Our findings are of immediate applicability
in modern analog quantum simulators and digital NISQ devices.
