‘Alas!’ said Aragorn. ‘Thus passes the heir of Denethor, Lord of the Tower of Guard! This is a bitter end. Now the Company is all in ruin. It is I that have failed. Vain was Gandalf’s trust in me. What shall I do now? Boromir has laid it on me to go to Minas Tirith, and my heart desires it; but where are the Ring and the Bearer? How shall I find them and save the Quest from disaster?’
He knelt for a while, bent with weeping, still clasping Boromir’s hand. So it was that Legolas and Gimli found him. - LotR III.1

A little to the left facing them stood she whom he had called Dernhelm. But the helm of her secrecy, had fallen from her, and her bright hair, released from its bonds, gleamed with pale gold upon her shoulders. Her eyes grey as the sea were hard and fell, and yet tears were on her cheek. A sword was in her hand, and she raised her shield against the horror of her enemy’s eyes.

And there stood Meriadoc the hobbit in the midst of the slain, blinking like an owl in the daylight, for tears blinded him; and through a mist he looked on Éowyn’s fair head, as she lay and did not move; and he looked on the face of the king, fallen in the midst of his glory, For Snowmane in his agony had rolled away from him again; yet he was the bane of his master.
Then Merry stooped and lifted his hand to kiss it, and lo! Théoden opened his eyes, and they were clear, and he spoke in a quiet voice though laboured.
‘Farewell, Master Holbytla!’ he said. ‘My body is broken. I go to my fathers. And even in their mighty company I shall not now be ashamed. I felled the black serpent. A grim morn, and a glad day, and a golden sunset!’
Merry could not speak, but wept anew. ‘Forgive me, lord,’ he said at last, ‘if I broke your command, and yet have done no more in your service than to weep at our parting.’

But Éomer leaped from the saddle, and grief and dismay fell upon him as he came to the king’s side and stood there in silence.
Then one of the knights took the king’s banner from the hand of Guthl‡f the banner-bearer who lay dead, and he lifted it up. Slowly Théoden opened his eyes. Seeing the banner he made a sign that it should be given to Éomer.
‘Hail, King of the Mark!’ he said. ‘Ride now to victory! Bid Éowyn farewell!’ And so he died, and knew not that Éowyn lay near him. And those who stood by wept, crying: ‘Théoden King! Théoden King!’
But Éomer said to them:

Mourn not overmuch! Mighty was the fallen,
meet was his ending. When his mound is raised,
women then shall weep. War now calls us!

Yet he himself wept as he spoke. ‘Let his knights remain here,’ he said; ‘and bear his body in honour from the field, lest the battle ride over it!

Imrahil, Prince of Dol Amroth, rode up and drew rein before them.
‘What burden do you bear, Men of Rohan?’ he cried.
‘Théoden King,’ they answered. ‘He is dead. But Éomer King now rides in the battle: he with the white crest in the wind.’
Then the prince went from his horse, and knelt by the bier in honour of the king and his great onset; and he wept. And rising he looked then on Éowyn and was amazed. ‘Surely, here is a woman?’ he said. ‘Have even the women of the Rohirrim come to war in our need?’ - All from LotR V.6. (bolds by squire)