In Sir Gawain and the Green Knight, the sense of honor displayed by the characters is chivalric and idealistic. The honor displayed is unrealistically demanding, which is appropriate for a medieval romance.
Gawain is presented as actually failing in the poem, because he flinches as the Green Knight's blade descends toward his neck. The Green Knight sees this as failure, as does Gawain. An honorable hero, it's inferred, should take this blow without flinching. This sense of honor is not realistic, but idealistic. It's supposed to be. Medieval romances are larger than life, as are romance heroes. Gawain also fails when he does not share the magic girdle with the Green Knight, even though the girdle may save his life. This, too, is idealistic. Who would give up the girdle?
Perfection in honor is expected: Gawain volunteers to take King Arthur's place when the Green Knight challenges Arthur; the Green Knight bares his neck when it's his turn to be beheaded; Gawain seeks out the Green Knight one year later when it's his turn to lose his head; Gawain resists temptation by rejecting the sexual advances of the Green Knight's wife.
Ironically, it is Gawain's failure that sets this poem apart from others of its kind. Medieval heroes are supposed to be perfectly honorable, even when the sense of honor depicted is rigid and impossibly difficult to adhere, too. Gawain's failure presents a hero that is more human, slightly imperfect. This is a step in literature toward eventually presenting human, flawed protagonists that more closely reflect actual human experience.