Can I get Simon to periodically e-mail me to reassure me it is still working?

Yes, you can do this by adding a test for a frequently-updating page, like http://www.timeanddate.com/worldclock/, which changes every second. Then check it at whatever frequency you want to be e-mailed, and have an E-mail notifier for changes. You can customize the e-mail message to say "I'm alive!" or whatever you like.