If I recall correctly,

/etc/init.d/jamf.tomcat start/stop/status

(choose one)
will return what you are looking for. Browsing to https://yourjss.com:8443 will also tell you something ;-) What more are you looking for?

I've used curl in the past to check that the site is reachable and readable.

Are you getting frequent tomcat crashes?

You could also use the new Health Check page:

https://your.jss.com:8443/healthCheck.html

JSS Health Check Docs

-Brad

I've got a scripted solution for monitoring my JSS's Tomcat, which regularly checks that Tomcat is running. If it's not, the following actions are taken:

1. Tomcat is restarted
2. I receive an email letting me know Tomcat has been restarted, along with other diagnostic information.

I have a post about this solution available from the link below:

https://derflounder.wordpress.com/2011/12/14/monitoring-the-casper-jss-tomcat-on-red-hat-linux/

The scripts are available on my GitHub repo via the link below:

https://github.com/rtrouton/rtrouton_scripts/tree/master/rtrouton_scripts/tomcat_monitoring