Recently, there has been increased interest in fair generative models. In this work,we conduct, for the first time, an in-depth study on fairness measurement, acritical component in gauging progress on fair generative models. We make threecontributions. First, we conduct a study that reveals that the existing fairnessmeasurement framework has considerable measurement errors, even when highlyaccurate sensitive attribute (SA) classifiers are used. These findings cast doubtson previously reported fairness improvements. Second, to address this issue,we propose CLassifier Error-Aware Measurement (CLEAM), a new frameworkwhich uses a statistical model to account for inaccuracies in SA classifiers. Ourproposed CLEAM reduces measurement errors significantly, e.g., 4.98%→0.62%for StyleGAN2 w.r.t. Gender. Additionally, CLEAM achieves this with minimaladditional overhead. Third, we utilize CLEAM to measure fairness in importanttext-to-image generator and GANs, revealing considerable biases in these modelsthat raise concerns about their applications. Code and more resources: https://sutd-visual-computing-group.github.io/CLEAM/.