Lindsay Haisley writes:

Something is happening inside OpenSSL. I think than OpenSSL is trying to find the remote server's certificate authority's certificate.

A lot of SMTP servers use self-signed certs, so certificate verification for SMTP isn't really useful. The default courierd settings have ESMTP_TLS_VERIFY_DOMAIN=0 and TLS_VERIFY_PEER=NONE. This allows TLS to proceed, but disables certificate verification. If you changed these settings in courierd, try reverting to these defaults and see what happens. I'm not actually sure if this is what triggers the error message. ENOENTs, as you've noted, are quite common and ordinary, you need to look for the one that immediately preceded the "No such file or directory". There may be another reason, but confirming that these settings are the default will eliminate that possibility.