I can't send any emails on one of my email accounts in Apple's mail application even though I can receive emails with this account. My other accounts send and receive. I have no problem sending from this account on my iPad or iPhone, so it's not the account, it's definitely the Mail application. My wife is having the same problem on her Macbook with her Gmail account. I've deleted the Keychain entries for the accounts, and then entirely deleted the accounts and created them again, and neither worked. I'm using a Macbook Pro running 10.8.3 with Mail version 6.3 Is anyone else having this problem?
Look in the Account settings in Apple Mail and look at the Outgoing Mail Server (SMTP) setting and see if it matches the correct mail service. (i.e. is it using the Gmail smtp server if it is a gmail account. Also, you can use the drop down list and select Edit SMTP Server List to select that particular SMTP server's settings. For Gmail it would be smtp.gmail.com and mine is set to use the default ports, has Authentication as password, and has my login credentials.
Hope this helps.