If your Apple Mail SMTP cannot send out email, below may help solve your Apple Mail issues.
1. At your Mail, open the Preferences under your Apple Menu
2. Select Accounts and then select the account from your list
3. At the Outgoing Mail Server Box choose “Edit Server List”
4. Server the server in question and choose the advance tab
5. Select Password from the Authentication Combo Box
6. Enter your username and password.
That should do the trick.