The growing demand for spatially detailed data to advance the Sustainable Development Goals agenda of ‘leaving no one behind’ has resulted in a shift in focus from aggregate national and province-based metrics to small areas and high-resolution grids in the health and development arena. Vaccination coverage is customarily measured through aggregate-level statistics, which mask fine-scale heterogeneities and ‘coldspots’ of low coverage. This paper develops a methodology for high-resolution mapping of vaccination coverage using areal data in settings where point-referenced survey data are inaccessible. The proposed methodology is a binomial spatial regression model with a logit link and a combination of covariate data and random effects modelling two levels of spatial autocorrelation in the linear predictor. The principal aspect of the model is the melding of the misaligned areal data and the prediction grid points using the regression component and each of the conditional autoregressive and the Gaussian spatial process random effects. The Bayesian model is fitted using the INLA-SPDE approach. We demonstrate the predictive ability of the model using simulated data sets. The results obtained indicate a good predictive performance by the model, with correlations of between 0.66 and 0.98 obtained at the grid level between true and predicted values. The methodology is applied to predicting the coverage of measles and diphtheria-tetanus-pertussis vaccinations at 5 × 5 km²in Afghanistan and Pakistan using subnational Demographic and Health Surveys data. The predicted maps are used to highlight vaccination coldspots and assess progress towards coverage targets to facilitate the implementation of more geographically precise interventions. The proposed methodology can be readily applied to wider disaggregation problems in related contexts, including mapping other health and development indicators.