You can have your server log files sent to an email address.

Edit the logwatch configuration file :

vi /etc/logwatch/conf/logwatch.conf ( if this file is empty , edit the following file)

vi /usr/share/logwatch/default.conf/logwatch.conf

find mailto and put the email address there.

Or you can create an alias for root.

Vi /etc/aliases

root: youremailaddress