Administrative data are being used ever more frequently in the production of official statistics. In many cases, available registers cannot meet all demands made by users of official statistics and therefore have to be supplemented by other data sources, most notably sample surveys. To ensure that the resulting statistics are of sufficient quality, it is necessary to evaluate their accuracy – in particular, their variances. In general, estimating the variance of an estimator based on combined administrative and survey data is not a trivial task. In this paper, a generic bootstrap method is described for this purpose. As a running example, we consider variance estimation for frequency tables in the Dutch virtual population Census, where mass imputation may be used to estimate missing values of educational attainment.