Você precisa usar a opção -prexit
:
Por exemplo,
openssl s_client -connect server:8443 -prexit
print session information when the program exits. This will always attempt to print out information even if the connection fails. Normally information will only be printed out once if the connection succeeds. This option is useful because the cipher in use may be renegotiated or the connection may fail because a client certificate is required or is requested only after an attempt is made to access a certain URL. Note: the output produced by this option is not always accurate because a connection might never have been established.