Political scientists interested in estimating how public opinion varies by constituency have developed several strategies for supplementing limited constituency survey data with additional sources of information. We present two evaluation studies in the previously unexamined context of British constituency-level opinion: an external validation study of party vote share in the 2010 general election and a cross-validation of opinion toward the European Union. We find that most of the gains over direct estimation come from the inclusion of constituency-level predictors, which are also the easiest source of additional information to incorporate. Individual-level predictors combined with post-stratification particularly improve estimates from unrepresentative samples, and geographic local smoothing can compensate for weak constituency-level predictors. We argue that these findings are likely to be representative of applications of these methods where the number of constituencies is large.