Child marriage is associated with bad outcomes for women and girls. Although many countries have raised the legal age of marriage to deter this practice, the incidence of early marriage remains stubbornly high. We develop a simple model to explain how enforcing minimum age-of-marriage laws creates differences in the share of women getting married at the legal cut-off. We formally test for these discontinuities using multiple rounds of the Demographic and Health Surveys (DHS) in over 60 countries by applying statistical tests derived from the regression discontinuity literature. By this measure, most countries are not enforcing the laws on their books and enforcement is not getting better over time. Separately, we demonstrate that various measures of age-of-marriage discontinuities are systematically related to with existing, widely-accepted measures of rule-of-law and government effectiveness. A key contribution is therefore a simple, tractable way to monitor legal enforcement using survey data. We conclude by arguing that better laws must be accompanied by better enforcement and monitoring in to delay marriage and protect the rights of women and girls.