Not to my knowledge. The closest example occurs near the beginning of Sir Gawain and the Green Knight, in which everyone at the Round Table is so stunned by the Green Knight's appearance and his challenge that no one moves at first to accept it, but when Gawain sees that Arthur himself is about to do so, he quickly moves to accept the challenge himself rather than let the entire Round Table be disgraced by leaving the King to fight his own duel.
I have to say that I don't think Beowulf and Arthur are very comparable, beyond being medieval kings. Arthur isn't really known for his heroic deeds beyond pulling the sword out of the stone. Instead, he's known for the court he established at Camelot, where the best knights in the world came to do gallant deeds in his name. He can be seen as a unifying force under whom heroic deeds are done, but for the most part he simply presides over them.
If you're using Malory's Le Morte d'Arthur (or one of its retellings) as your source for Arthur, you CAN point out that Arthur and Beowulf both die alone but for one companion. While Beowulf's followers panicked and fled, Arthur's have been killed.
If you've read Sir Gawain and the Green Knight, would you consider doing your comparison on Beowulf and Gawain instead? The outstanding thing about both of them, to me, is that they have higher, stricter concepts of honor than do the people around them. Look at the incident, between the two major adventures, in which Beowulf is first offered the Geatish throne and the one in which Gawain returns to Camelot and tells his fellow knights how he has disgraced himself.