Receiver operating characteristic (ROC) curves are frequently used to assess the usefulness of diagnostic markers. When several diagnostic markers are available, they can be combined by a best linear combination: that is, when the area under the ROC curve of this combination is maximized among all possible linear combinations. This maximal area is the generalized ROC criterion, which provides a measure of how effective the combination of the markers is. This criterion needs to be estimated from the data, and is usually evaluated against single markers. In the present paper, we provide confidence intervals for the generalized ROC criterion under the assumption of homogeneous covariance matrices, derive an approximation for the heterogeneous covariance matrices case, and evaluate the approximation via a simulation study. Finally, we present an illustrative example.