A method is proposed for combining information from several emergent constraints into a probabilistic estimate for a climate sensitivity proxy Y such as equilibrium climate sensitivity (ECS). The method is based on fitting a multivariate Gaussian PDF for Y and the emergent constraints using an ensemble of global climate models (GCMs); it can be viewed as a form of multiple linear regression of Y on the constraints. The method accounts for uncertainties in sampling this multidimensional PDF with a small number of models, for observational uncertainties in the constraints, and for overconfidence about the correlation of the constraints with the climate sensitivity. Its general form (Method C) accounts for correlations between the constraints. Method C becomes less robust when some constraints are too strongly related to each other; this can be mitigated using regularization approaches such as ridge regression. An illuminating special case, Method U, neglects any correlations between constraints except through their mutual relationship to the climate proxy; it is more robust to small GCM sample size and is appealingly interpretable. These methods are applied to ECS and the climate feedback parameter using a previously published set of 11 possible emergent constraints derived from climate models in the Coupled Model Intercomparison Project (CMIP). The ±2σ posterior range of ECS for Method C with no overconfidence adjustment is 4.3 ± 0.7 K. For Method U with a large overconfidence adjustment, it is 4.0 ± 1.3 K. This study adds confidence to past findings that most constraints predict higher climate sensitivity than the CMIP mean.