I changed my email password on the Shaw website but when I entered it into the Mail app on my Mac it responded with "Unable to verify account password".
I don't know why this happens when the Shaw mail password is changed, but the solution seems to be to delete the Shaw account on the Mac side and add a new account. The computer then automatically connects to Shaw and downloads the Inbox/Sent/Drafts mail.
@JBlackburn -- by "account", do you mean an "account" within your Mac Mail app? Each "account" will access a different mail-server, with different credentials, e.g. "JoeB(at)Yahoo" & "BJ(at)Gmail" IDs.