[/etc/hosts]
127.0.0.1       localhost.localdomain localhost
::1             localhost6.localdomain6 localhost6
<serverip> <machinename>.<mydomain>.<tld>
<serverip> <mydomain>.<tld>

# The following lines are desirable for IPv6 capable hosts
::1 ip6-localhost ip6-loopback
fe00::0 ip6-localnet
ff00::0 ip6-mcastprefix
ff02::1 ip6-allnodes
ff02::2 ip6-allrouters
ff02::3 ip6-allhosts

---
Using postfix -

[/etc/postfix/main.cf]
...
myhostname = <machinename>.<mydomain>.<tld>
mydomain = <mydomain>.<tld>
myorigin = $mydomain
...
relay_domains = hash:/etc/postfix/relay_domains
...
readme_directory = /usr/share/doc/postfix-2.10.1/README_FILES
smtpd_sasl_local_domain = $myhostname
smtpd_sasl_auth_enable = yes
smtpd_sasl_security_options = noanonymous
broken_sasl_auth_clients = yes
smtpd_sasl_authenticated_header = yes
smtpd_recipient_restrictions =
        check_sender_access hash:/etc/postfix/sender_access,
        permit_sasl_authenticated,
        permit_mynetworks,
        reject_unauth_destination,
        regexp:/etc/postfix/banned-regexp
        #,check_relay_domains
mynetworks = 127.0.0.0/8
inet_protocols=ipv4
smtpd_tls_auth_only = no
smtp_use_tls = yes
smtpd_use_tls = yes
smtp_tls_note_starttls_offer = yes
smtpd_tls_key_file = /etc/postfix/ssl/smtpd.key
smtpd_tls_cert_file = /etc/postfix/ssl/smtpd.crt
smtpd_tls_CAfile = /etc/postfix/ssl/cacert.pem
smtpd_tls_loglevel = 1
smtpd_tls_received_header = yes
smtpd_tls_session_cache_timeout = 3600s
tls_random_source = dev:/dev/urandom
home_mailbox = Maildir/
unverified_sender_reject_code = 550
#parent_domain_matches_subdomains = debug_peer_list,fast_flush_domains,mynetworks,permit_mx_backup_networks,qmqpd_authorized_clients,relay_domains,smtpd_access_maps
parent_domain_matches_subdomains = mynetworks,permit_mx_backup_networks,smtpd_access_maps
#,relay_domains
mailbox_command =

smtp_sasl_path = smtp
smtp_sasl_auth_enable = yes
smtp_sasl_security_options = noanonymous #noplaintext
smtp_sasl_password_maps = hash:/etc/postfix/sasl_passwd
smtpd_sender_restrictions =
    permit_mynetworks,
    reject_non_fqdn_sender,
    reject_unknown_sender_domain,
    permit
sendmail_path = /usr/sbin/sendmail
data_directory = /var/lib/postfix

TBH, I haven't looked at this in years, so it may not be configured optimally.

[/etc/postfix/mydestinations]
/localhost/                            ACCEPT
/<mydomain>\.<tld>/                    ACCEPT
/.*\.<mydomain>\.<tld>/                ACCEPT

[/etc/postfix/relay_domains]
<machinename>.<mydomain>.<tld>       OK
*.<mydomain>.<tld>                   OK
<mydomain>.<tld>                     OK

[/etc/postfix/sasl_passwd]
smtp.gmail.com:587      <gmailnick>@gmail.com:<mygmailpass>

These files need to be hashed:
/usr/sbin/postmap hash:/etc/postfix/relay_domains
/usr/sbin/postmap hash:/etc/postfix/mydestinations
/usr/sbin/postmap hash:/etc/postfix/sasl_passwd

After changing any of these files and hashing them, you need to restart postfix to pick up the changes.

/sbin/service dovecot restart #I don't remember if this is necessary
/sbin/service postfix restart

Then I run a quick php script:

<?php
$to      = '<mynick>@newrelic.<mydomain>.<tld>';
$subject = 'Super Serious Offer';
$message = 'hello there you, do you scam?';
$headers = 'From: [email protected]' . "\r\n";
mail($to, $subject, $message, $headers);
?>

Then I test from say a gmail or yahoo mail account. There's additional work to get gmail working, iirc.

This is also how I test blocking domains, which can be done:
vi /etc/postfix/banned-regexp

/<mynick>@ably\.<mydomain>\.<tld>/ REJECT

I have lots of this. Add a line then restart postfix.
/sbin/service postfix restart

Test with the php script and see if it arrives.