I report medium-resolution spectroscopic observations of six H emission-line stars proposed by Meyer et al. (1993) to be T Tauri stars formed in the vicinity of the B1 giant Sco, a bright member of the Sco-Cen OB association. Using spectroscopic criteria which are distance-independent, I classify these stars in different premain-sequence (PMS) classes. Taking data from the literature, a number of stars detected by X-ray observations around other B-type members of Sco-Cen are also classified. The current census of 'bona fide' low-mass PMS stars identified in about 9 sq deg in Sco-Cen includes two classical T Tauri stars, 18 weak T Tauri stars (WTTSs), and 10 post-T Tauri stars (PTTSs). The presence of a mixture of T Tauri and post T Tauri stars implies that previous results based on isochrone fitting that indicated an extremely young age for the Sco-Cen PMS low-mass population are incorrect. A distance of about 125 pc for Sco-Cen, instead of the 160 pc used in previous works, is consistent with the Hipparcos parallaxes for many of the B-type stars and would lead to older H-R diagram ages. Taking into account that PTTSs are generally fainter and harder to identify than WTTSs, I argue that the WTTS-to-PTTS ratio in Sco-Cen may be of order unity. This result suggests that the low-mass stars of the OB association span an age range similar to the B-type members the low- and high-mass star populations are essentially coeval.