  Quantum-simulator hardware promises new insights into problems from particle
and nuclear physics. A major challenge is to reproduce gauge invariance, as
violations of this quintessential property of lattice gauge theories can have
dramatic consequences, e.g., the generation of a photon mass in quantum
electrodynamics. Here, we introduce an experimentally friendly method to
protect gauge invariance in $\mathrm{U}(1)$ lattice gauge theories against
coherent errors in a controllable way. Our method employs only single-body
energy-penalty terms, thus enabling practical implementations. As we derive
analytically, some sets of penalty coefficients render undesired gauge sectors
inaccessible by unitary dynamics for exponentially long times, and, for
few-body error terms, with resources independent of system size. These findings
constitute an exponential improvement over previously known results from
energy-gap protection or perturbative treatments. In our method, the
gauge-invariant subspace is protected by an emergent global symmetry, meaning
it can be immediately applied to other symmetries. In our numerical benchmarks
for continuous-time and digital quantum simulations, gauge protection holds for
all calculated evolution times (up to $t>10^{10}/J$ for continuous time, with
$J$ the relevant energy scale). Crucially, our gauge-protection technique is
simpler to realize than the associated ideal gauge theory, and can thus be
readily implemented in current ultracold-atom analog simulators as well as
digital noisy intermediate scale quantum (NISQ) devices.
