nmap imap.theirserver.com

openssl s_client -connect imap.theirserver.com:port
openssl s_client -crlf -showcerts -starttls imap(or smtp) connect imap.theirserver.com:port  (if the port is unencrypted)

140735820493760:error:0200203C:system library:connect:Operation timed
out:crypto/bio/b_sock2.c:108: 140735820493760:error:2008A067:BIO
routines:BIO_connect:connect error:crypto/bio/b_sock2.c:109:
connect:errno=60