It:safari

Allowing Web browsers to run Java using local files

A complete set of settings is available here.

in Mavericks

1. Open a local file in Safari (essential)
2. Safari/Preferences/Security
3. Internet plug-ins: allow and then Manange Web site Settings
4. Select Java from list on the left
5. Local documents: Always Allow (this does not appear unless you have loaded a local file)

Your security settings have blocked a self-signed application from running?

In Mavericks with Java 7/60 or 8/05

1. Apple menu/System preferences/Java
2. Security/Edit site list (for the exceptions Site list)
3. Add the URL of the site associated with the error message you got (you may have to type this by hand)
4. Refresh the page. You will now get a different message, warning that you are about to run an insecure applet. If you trust it, say yes!