I configured the exim4 server to use a smarthost (my email company). I also turned on the header rewriting so that the address matches the one sent from the email company's domain. This domain requires SSL, and exim4 should, as far as I understand the documentation handle this correctly.
I switched on the header rewriting because I heard that smarthost will usually decline mail coming from a dynamic address assigned by a provider, unless the header is what is used by that domain.
Yet, I am unable to send anything. The process of sending email proceeds like this:
R: smarthost for firstname.lastname@example.org
T: remote_smtp_smarthost for email@example.com
LOG: retry_defer MAIN
== firstname.lastname@example.org R=smarthost T=remote_smtp_smarthost defer (-53): retry time not reached for any host