Yes, they did. It is important to note that none ever actively tried to carry out something like the Kenmu or Meiji restorations to depose the Bakufu and restore rule from a central court, which was really not a realistic prospect anyway. Instead, the Emperor/court tried to reassert some sort of political and diplomatic influence over whoever was the central power at the time as well as whichever of the many competing locals that would listen. After the end of the Sengoku Jidai, what power gained during the chaotic warfare was clawed back, and though the Emperor/court successfully resisted the new Bakufu's attempt through marriage to put someone of Tokugawa blood on the throne and control court politics, that's as far as they could do.

See here for more details. The part about the Muromachi Bakufu is a bit outdated, but the part about the court should still stand.