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We present new period-age (PA) and period-age-color (PAC) relations for fundamental and first-overtone classical Cepheids. Current predictions rely on homogeneous sets of evolutionary and pulsation models covering a broad range of stellar masses and chemical compositions. We found that PA and PAC relations present a mild dependence on metal content. Moreover, the use of different PA and PAC relations for fundamental and first-overtone Cepheids improves the accuracy of age estimates in the short-period (logP<1) range (old Cepheids), because they present smaller intrinsic dispersions. At the same time, the use of the PAC relations improves the accuracy in the long-period (logP≥1) range (young Cepheids), since they account for the position of individual objects inside the instability strip. We performed a detailed comparison between evolutionary and pulsation ages for a sizable sample of LMC (15) and SMC (12) clusters which host at least two Cepheids. In order to avoid deceptive uncertainties in the photometric absolute zero point, we adopted the homogeneous set of B, V, and I data for clusters and Cepheids collected by OGLE. We also adopted the same reddening scale. The different age estimates agree at the level of 20% for LMC clusters and of 10% for SMC clusters. We also performed the same comparison for two Galactic clusters (NGC 6067, NGC 7790), and the difference in age is smaller than 20%. These findings support the use of PA and PAC relations to supply accurate estimates of individual stellar ages in the Galaxy and in external Galaxies. The main advantage of this approach is its independence from the distance.