I understand this will be called when the app is backgrounded *and* the system needs to kill the process. What I find in the emulator is there are apparently enough resources such that the app is restored immediately upon being foregrounded without needing to make this call. So how can I test it please?

This call is made when switching orientation, for example a video player application is running and the user tips the device to view the video landscape, this results in the Activity being torn down and another created.

The video player uses this call to remember the position of the video so that when the new activity starts the video resumes.

Another way to force onSaveInstanceState() to be called is to set up the emulator to kick your app out of memory. I find this is a more realistic way to test: your app gets killed, and all the variables are destroyed. To make this happen, in the emulator, go to Dev Tools; Development Settings; click on the drop-down box "app process limit", and set it to 1. Start your app, hit home, then start contacts or some simple app. You may see a kill message in logcat.

That's a great tip I didn't know about - sincere thanks!