Significant progress in understanding quarkonium production requires improved polarization measurements, fully considering the intrinsic multidimensionality of the problem. We propose a frame-invariant formalism which minimizes the dependence of the measured result on the experimental acceptance, facilitates the comparison with theoretical calculations, and provides a much needed control over systematic effects due to detector limitations and analysis biases. This formalism is a direct and generic consequence of the rotational invariance of the dilepton decay distribution and is independent of any assumptions specific to particular models of quarkonium production.