Many monitoring services support and provide agents to monitor all kinds of properties on your servers as well as custom checks for things/metrics they don't support natively already.
- Install the agent and you should get many useful metrics.
In addition even basic/trivial web site monitoring services allow you to define additional URL's to check.
Consider setting up a (password protected) monitoring area on your website where you can deploy trivial web services for such custom monitoring.
Then for example have your backup script log a date/time, success or failure and whatever else you deem important to a status file and create a trivial web service that parses that file, something along the lines of the pseudo code below:
if ( modification_time( backup_log_file ) > 36 hours)
then
send http_response_header = 500
send http_response_body = "RED: the last successful backup is more than 36 hours old"
fi
if ( backup_log_file CONTAINS_STRING "success" )
then
send http_response_header = 200
send http_response_body = "GREEN: the last backup was successful"
else
send http_response_header = 500
send http_response_body = "RED: the last backup failed"
fi