Livia Drusilla advised the Emperor Augustus on the policies of ruling an Empire, and he took her advice quite seriously. I do not think he would've been able to rule as well as he did without her able assistance. She also played a role in the administration of her son Tiberius, something which he came to resent, and their contentious relationship may have been one of the reasons why he ultimately withdrew from Rome to Capri. All of the Julio-Claudian rulers were her direct descendants. She would eventually be deified by her grandson Claudius after he became Emperor. I'd call her the strongest and, because of what was deeded to her from Augustus (she received one-third of his immense wealth) perhaps the richest and most powerful of all the Roman Empresses.
The other impressive Empress, though not of Rome, is that of Theodora. The wife of the Emperor Justinian, she ruled as empress regent. She was brilliant and sharp, and her advice was sound, Justinian even calling her the partner in his deliberations. The most crucial role she ever played was when she saved her husband's reign by standing fast during the Nika Riots. Justinian was ready to flee the city, an action that would've almost certainly cost him his throne if not his life. But she stood firm and told him that "royal purple is the noblest shroud" in reference to the burial winding sheet that deceased Emperors were wrapped in. So Justinian mustered himself up and sent in Belisarius, who crushed the revolt and restored order. She participated not only in the rebuilding of the burned city, including the Hagia Sophia, but also the Emperor's religious and legal reforms, being especially particular about him increasing the rights of women. She, too, like Livia, has been deified in her own way, being a saint under the Eastern Orthodox Church.
