Modulating the polarization of excitation light, resolving the polarization of emitted fluorescence, and pointspread function (PSF) engineering have been widely leveraged for measuring the orientation of single molecules.Typically, the performance of these techniques is optimized and quantified using the Cramér-Rao bound (CRB),which describes the best possible measurement variance of an unbiased estimator. However, CRB is a localmeasure and requires exhaustive sampling across the measurement space to fully characterize measurementprecision. We develop a global variance upper bound (VUB) for fast quantification and comparison of orientationmeasurement techniques. Our VUB tightly bounds the diagonal elements of the CRB matrix from above; VUBoverestimates the mean CRB by ～34%. However, compared to directly calculating the mean CRB over orientationspace, we are able to calculate VUB ～1000 times faster.
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