“‘I wished to be loved by another,’ she answered. 'But I desire no man

“‘I wished to be loved by another,’ she answered. 'But I desire no man’s pity.’

'That I know,’ he said. 'You desired to have the love of the Lord Aragorn. Because he was high and puissant, and you wished to have renown and glory and to be lifted far above the mean things that crawl on the earth. And as a great captain may to a young soldier he seemed to you admirable. For so he is, a lord among men, the greatest that now is. But when he gave you only understanding and pity, then you desired to have nothing, unless a brave death in battle. Look at me, Éowyn!’

And Éowyn looked at Faramir long and steadily; and Faramir said: 'Do not scorn pity that is the gift of a gentle heart, Éowyn! But I do not offer you my pity. For you are a lady high and valiant and have yourself won renown that shall not be forgotten; and you are a lady beautiful, I deem, beyond even the words of the Elven-tongue to tell. And I love you. Once I pitied your sorrow. But now, were you sorrowless, without fear or any lack, were you the blissful Queen of Gondor, still I would love you. Éowyn, do you not love me?’

Then the heart of Éowyn changed, or else at last she understood it. And suddenly her winter passed, and the sun shone on her.

‘I stand in Minas Anor, the Tower of the Sun,’ she said; ‘and behold the Shadow has departed! I will be a shieldmaiden no longer, nor vie with the great Riders, nor take joy only in the songs of slaying. I will be a healer, and love all things that grow and are not barren.’ And again she looked at Faramir. 'No longer do I desire to be a queen,’ she said.

Then Faramir laughed merrily. 'That is well,’ he said; 'for I am not a king. Yet I will wed with the White Lady of Rohan, if it be her will. And if she will, then let us cross the River and in happier days let us dwell in fair Ithilien and there make a garden. All things will grow with joy there, if the White Lady comes.’

'Then must I leave my own people, man of Gondor?’ she said. 'And would you have your proud folk say of you: "There goes a lord who tamed a wild shieldmaiden of the North! Was there no woman of the race of Númenor to choose?”’

'I would,’ said Faramir. And he took her in his arms and kissed her under the sunlit sky, and he cared not that they stood high upon the walls in the sight of many. And many indeed saw them and the light that shone about them as they came down from the walls and went hand in hand to the Houses of Healing.“

–J.R.R. Tolkien, The Lord of the Rings: The Return of the King, "The Steward and the King”

“Eowyn: It is possible to love more than one person (of the other sex) at the same time, but in a different mode and intensity. I do not think that Eowyn’s feelings for Aragorn really changed much; and when he was revealed as so lofty a figure, in descent and office, she was able to go on loving and admiring him. He was old, and that is not only a physical quality: when not accompanied by any physical decay age can be alarming or awe-inspiring. Though not a 'dry nurse’ in temper, she was also not really a soldier or 'amazon’, but like many brave women was capable of great military gallantry at a crisis.

I think you misunderstand Faramir. He was daunted by his father: not only in the ordinary way of a family with a stern proud father of great force of character, but as a Númenórean before the chief of the one surviving Númenórean state. He was motherless and sisterless (Eowyn was also motherless), and had a 'bossy’ brother. He had been accustomed to giving way and not giving his own opinions air, while retaining a power of command among men, such as a man may obtain who is evidently personally courageous and decisive, but also modest, fair-minded and scrupulously just, and very merciful. I think he understood Eowyn very well.

…

Criticism of the speed fo the relationship or 'love’ of Faramir and Eowyn. In my experience feelings and decisions ripen very quickly (as measured by mere 'clock-time’, which is actually not justly applicable) in periods of great stress, and especially under the expectation of imminent death. And I do not think that persons of high estate and breeding need all the petty fencing and approaches in matters of 'love’. This tale does not deal with a period of 'Courtly Love’ and its pretences; but with a culture more primitive (sc. less corrupt) and nobler.”

–J.R.R. Tolkien, The Letters of J.R.R. Tolkien, “244” (From a draft to a reader of The Lord of the Rings [A fragment at the top of which Tolkien has written: 'Comments on a criticism (now lost?) concerning Faramir & Eowyn…’.])