How do “Lines Composed a Few Miles from Tintern Abbey” and “Ode to a Grecian Urn” relate to the concepts of Romanticism?

Because both Wordsworth's and Keats's poems take as their subject "emotion recollected in tranquility," as Wordsworth defines poetry, they clearly relate to many of the concepts of Romanticism.
Romanticism was a literary movement that constituted a reaction to Neoclassicism and its order, restraint, decorum, reason, and harmony. This movement of Romanticism emphasized imagination, freedom, emotion, fancy, and the beauty of the untamed world. Romanticism also celebrated the rights of all individuals, the innate nobility of the common man, and the beauty of pastoral life and love of Nature.

"Lines Composed a Few Miles Above Tintern Abbey" 

A great lover of nature, William Wordsworth composed this poem during his second visit to the valley of the River Wye and the ruins of Tintern Abbey, which was once a great church in the Middle Ages.
As is characteristic of Romantic poems, Wordsworth employs blank verse (unrhymed iambic pentameter).
The importance of emotion and the imagination is clearly stressed in this poem that describes the speaker's innermost feelings and his delight in all that he sees.
There is a celebration of the beauty of nature as the poet describes the landscape with the "soft inland murmur" of mountain springs, the "beauteous farms," and the hedgerows and woods that are "all clad in one green hue."
The speaker also feels restored in spirit by nature and its beauty. This awe-inspiring experience leads him to the sublime, a realm of consciousness beyond rational thought:

And I have feltA presence that disturbs me with the joyOf elevated thoughts; a sense sublimeOf something far more deeply interfused....
"Ode to a Grecian Urn"

Like Wordsworth's poem, Keats's ode focuses on the narrator's inner world and his experience of beauty.
Keats's poem expresses an interest in the past, a characteristic of Romanticism.
This poem clearly celebrates beauty and the imagination.
There is frequent use of personification, a technique often used by Romantics, as the speaker imagines that the figures move.
Exercising much imagination, the speaker also demonstrates an emotional interest in the artistry of the urn. As the speaker studies the scene on the Grecian urn, it captures his imagination. For instance, he imagines hearing the "happy melodist" who is "Forever piping songs forever new." 
Indeed, with an emphasis on the individual feelings of the speaker who views the painted scene, there is a sense of the urn's holding a spirit that runs through all things. Therefore, although the images are frozen on the urn, the viewer can still imagine the conclusion of the activities depicted by the artist. In this way, the viewer is empowered to imagine his own responses:

Heard melodies are sweet, but those unheard        Are sweeter; therefore, ye soft pipes, play on....

The melodies that the viewer imagines are sweeter than those that might have really been heard. In an examination of his feelings, the speaker studies the two lovers who are almost embracing. As he does so, he realizes that while the lovers will never actually embrace, in the world painted on the urn they forever experience the exciting anticipation of their kiss.
Emphasizing imagination over reason, the speaker concludes that the power of art is that it preserves the moment and communicates the truths of human experience.