I have looked at a lot of websites under the keywords Cadwalader, Cadwallader, and Cadwaldr. King Cadwalader was the last Welsh King. Like King Arthur, he symbolized Celtic resistance to Anglo-Saxon conquest. He married an Anglo-Saxon who was sister of the King of Mercia. Although his name means Battlefield Leader, he died of pestilence in 664. I have not read how King Edward's coat of arms came to incorporate King Cadwalder's banner. Perhaps it was a way of acknowledging the union of Wales and England. The name was used even during the centuries that Romans occupied Great Britain. The hypothesis that the surname Caldwell derives from Cadwalader, a Celtic name, runs counter to the evidence I presented, showing the derivation of Caldwell from Anglo-Saxon words, caelde weille, meaning cold spring-fed source of water welling up from the earth, i.e, artesian well. Tom's conjecture does have plausibility, however. He says that there are links between Caldwell and Calwaldr families. I just feel it is a viscoelastic theory that has been stretched to fit the facts, but ruptures when given a tug, just like Silly Putty.