According to the documentation, if DEBUG is set to False and something is provided under the ADMINS setting, Django will send an email
While likely not ideal, I have found using Gmail as the SMTP host works just fine. There is a useful guide at nathanostgard.com.
Feel free to post your relevant settings.py sections (including EMAIL_*, SERVER_EMAIL, ADMINS (just take out your real email), MANAGERS, and DEBUG) if you want an extra set of eyes to check for typos!