...the grimness left his face, and he looked like one who had laboured in sleepless pain for many nights. 'Nay, my friends, I am the lawful master of the Stone, and I had both the right and the strength to use it, or so I judged. The right cannot be doubted. The strength was enough - barely.'
The Passing of the Grey Company, ROTK Book V chapter II


The Dark Lord's awareness when it seized upon him was a grip like a vise, and it burned.

Who are you?

When Aragorn did not respond the power that held him intensified; flames rose high around him, hungry to consume him, render his being into ashes and dust. But Aragorn thought of the Pillars of Argonath, which might wear away from the long caresses of wind and water and time but would never be undone by fire, and he made his strength the strength of tall cold stone, and he remained silent. He felt Sauron's bafflement and the blaze of rage that could find no purchase to subdue his will, then knew, as the fires around him banked down to satisfied embers, that he was recognised.

Elessar.

Claws raking through flesh would have been more kind than Aragorn's name spoken by the Enemy, but he flinched not, nor did he speak.

So you come to me at last.

The force of Sauron's words beat upon Aragorn, each one a dreadful blow. He would not bend. Keeping one hand upon the Palantir he drew Anduril from its sheath and held it upright before him; the blade glittered with a pure cold light of its own. Between its brightness and Aragorn's own fell gaze Sauron writhed for a moment as if stung, and the heir of Elendil bent all his will to cast his Enemy from the Orthanc-stone.

The sound that came from the Enemy then was a scream; it was a great shrieking cry like that of a Nazgul, magnified in might a hundred-fold. It clove Aragorn to his bones, tore sinew from sinew, and shivered his flesh into a thousand pieces, yet implacable he would not give up the fight. Now the scream no longer came from Sauron, but in the voices of all those Aragorn loved most dearly in the world; behind and beneath these there rose a terrible chorus of despair drawn out from the throats of all living things as they burned away and were consumed by utter blackness. Yet Aragorn fought on: beyond reason and beyond fear, beyond hope or strength, until at last the struggle brought him to his knees before the Palantir. It was beyond enduring and he endured it, bracing himself with one hand against the hard ground, Anduril clasped still in his unfeeling fingers. The very air seemed to have turned to flame, and his lungs were burning.

But he felt the Enemy's growing doubt and wondering fear at the strength of this silent challenge from a son of Numenor, and in the face of his grim determination Sauron at last fell back before him and withdrew his awareness from the Palantir. It was done; it was done. He could breathe again, shocking himself with his own heaving gasps; cool air had never been so welcome nor so sweet. A thought came to him: If I had the Ring, indeed not even the Dark Lord himself could stand before me. But recognizing the peril of such thought he struck it from him as swiftly as it had come and stood, slowly, painfully, to sheathe the sword.

The Orthanc-stone lay gleaming, the black orb reflecting his face back to him in strange ways, grey-hued. It was his, and his work with it this night was not yet done.