The Mail App on my MacBook Pro and my iPhone does not let me send emails out

About a month ago, I stopped being able to send outgoing mail from my desktop and my phone. I'm able to receive mail just fine. I've checked all the settings to make sure the match with my email service provider and have even removed and re-created the accounts. Still having the same issue. There is no problem when I use webmail from my email service provider, I just can't send mail using Apple Mail! Please help! It's incredibly frustrating!!!

[Re-Titled by Moderator]