Summary: There are strong reasons to believe that global symmetries of quantum theories cannot be exact in the presence of gravity. While this has been argued at the qualitative level, establishing a quantitative statement is more challenging. In this work we take new steps towards quantifying symmetry violation in EFTs with gravity. First, we evaluate global charge violation by microscopic black holes present in a thermal system, which represents an irreducible, universal effect at finite temperature. Second, based on general QFT considerations, we propose that local symmetry-violating processes should be faster than black hole-induced processes at any sub-Planckian temperature. Such a proposal can be seen as part of the “swampland” program to constrain EFTs emerging from quantum gravity. Considering an EFT perspective, we formulate a conjecture which requires the existence of operators violating global symmetry and places quantitative bounds on them. We study the interplay of our conjecture with emergent symmetries in QFT. In models where gauged U(1)’s enforce accidental symmetries, we find that constraints from the Weak Gravity Conjecture can ensure that our conjecture is satisfied. We also study the consistency of the conjecture with QFT models of emergent symmetries such as extradimensional localization, the Froggatt-Nielsen mechanism, and the clockwork mechanism.