Poor Arthur throughout the whole thing keep begging Sir Ector and Kay not to prostrate themselves before him in that adorable squeaky voice of his.
There's one just before. When Ector, Kay and most of the lords start arguing with each other to try to pull the sword from the stone, Sir Pellinore and an unnamed Lord come to Arthur's defense, claiming that the boy deserves to try first, since he was the one who told them about the sword.
In fact, the entire scene with Arthur and the girl squirrel, untilthe end.
Despite his cranky and sarcastic demeanor Archimedes does have several small moments where he shows that he cares for Wart and Merlin, such as when he saves Wart from the pike, gives advice to Merlin during the wizard's duel with Mim and congrats Wart when he becomes Kay's squire, and at the end, he rejoices when Wart is declared king.
As Arthur is left exacerbated by his new title, Merlin returns from his 10-Minute Retirement quite happy with the turn of events, returning to his mentor role and giving Wart encouraging words about his future as king.