First, make sure /etc/mail/access includes: 

AuthInfo:smtp.critsend.com "U:CritSendUsername" "P:CritSendPassword" "M:PLAIN"


You need then to install sendmail, which you can do using the following command:


yum install sendmail-cf

Go to your mail folder and configure your access file:


cd /etc/mail
echo "AuthInfo:smtp.critsend.com \"U:YourCritSendUsername\" \"P:YourCritSendPassword\" \"M:PLAIN\"" > access
makemap hash access.db < access

Finally, add the following text to /etc/mail/sendmail.mc

define(`SMART_HOST', `smtp.critsend.com')dnl
dnl #FEATURE(`access_db', `hash -T -o /etc/mail/access.db < /etc/mail/access')dnl
FEATURE(`authinfo', `hash /etc/mail/access.db')dnl
define(`RELAY_MAILER_ARGS', `TCP $h 587')dnl
define(`ESMTP_MAILER_ARGS', `TCP $h 587')dnl
define(`confAUTH_MECHANISMS', `EXTERNAL GSSAPI DIGEST-MD5 CRAM-MD5 LOGIN PLAIN')dnl

Don't forget to restart sendmail:


/etc/init.d/sendmail restart