Update /etc/exim4/update-exim4.conf.conf so that it looks like:

dc_eximconfig_configtype='smarthost'
dc_other_hostnames=''
dc_local_interfaces='127.0.0.1'
dc_readhost='your.server.name'
dc_relay_domains=''
dc_minimaldns='false'
dc_relay_nets=''
dc_smarthost='smtp.critsend.com::587'
CFILEMODE='644'
dc_use_split_config='false'
dc_hide_mailname='true'
dc_mailname_in_oh='true'
                

Set your password and username to be your CritSend username and password: 

*:YourCritSendUsername: YourCritSendPassword
                

Update /etc/exim4/exim4.conf.localmacros (create the file if it doesn't already exist):

MAIN_TLS_ENABLE= 1

Restart your Exim server.