Childhood rubella infection in early pregnancy can lead to fetal death or congenital rubella syndrome (CRS) with multiple disabilities. Reduction of transmission via universal vaccination can prevent CRS, but inadequate coverage may increase CRS numbers by increasing the average age at infection. Consequently, many countries do not vaccinate against rubella. The World Health Organization recommends that for safe rubella vaccination, at least 80% coverage of each birth cohort should be sustained. The nonlinear relationship between CRS burden and infection dynamics has been much studied; however, how the complex interaction between epidemic and demographic dynamics affects minimum safe levels of coverage has not been quantitatively evaluated across scales necessary for a global assessment. We modelled 30-year CRS burdens across epidemiological and demographic settings, including the effect of local interruption of transmission via stochastic fadeout. Necessary minimum vaccination coverage increases markedly with birth and transmission rates, independent of amplitude of seasonal fluctuations in transmission. Susceptible build-up in older age groups following local stochastic extinction of rubella increased CRS burden, indicating that spatial context is important. In low birth-rate settings, 80% routine coverage is a conservative guideline, particularly if supplemented with campaigns and vaccination of women of childbearing age. Where birth and transmission rates are high, immunization coverage must be well above 80% and campaigns may be needed. Policy-makers should be aware of the potential negative effect of local extinction of rubella, since heterogeneity in vaccination coverage will shape extinction patterns, potentially increasing CRS burdens.