AppHarbor doesn't offer SMTP support directly, and many IP addresses being used for Amazon EC2 is blocked in spam directories, it wouldn't be a good solution anyway.
For sending email, you can sign up with one of the following:
In addition to these services, you can use Gmail or Google Apps for sending out a smaller number of emails, as well as external SMTP servers such as AuthSMTP.
If you use the legacy Mailgun add-on (no longer available), AppHarbor will automatically inject the relevant SMTP configuration. This lets you send emails like this:
var smtpClient = new SmtpClient();