The Presidential TARDISes were TARDISes intended for use by the President of the High Council. Romana II found them all to be lacking in character. (AUDIO: Square One)
Romana and Mephistopheles Arkadian travelled to Gryben in a TARDIS from the TARDIS bay. (AUDIO: Weapon of Choice) Days later, Romana used one of the Presidential TARDISes to travel to the fake temporal summit and escaped from the planetoid with Leela and an unconscious V'rell inside. (AUDIO: Square One)
Narvin had "Torvald" escort Romana to a Presidential TARDIS to keep her out of his way, but she instead materialised it in front of the Vienna to Calais Transcontinental Express to scare them, dematerialising at the last moment. (AUDIO: A Blind Eye)
Romana used a Presidential TARDIS to take herself and Leela to Davidia (AUDIO: Spirit) and, after scrambling the imprimaturs, briefly used Wynter's TARDIS instead due to it being the only operational timeship on Gallifrey. (AUDIO: Fractures)
"The President's TARDIS" was sabotaged by the Eleven and destroyed by the Sonomancer with the President, Chancellor Jerasta, and an aide aboard. (AUDIO: Songs of Love)