For security reasons, you should not be storing production setting values in source control. But this means that by default, you don't have your own backup of the values for your live, production settings.

What if you want to store a copy of your settings (e.g. along with the artifacts) in a secure location for each version of the software you release?

There doesn't currently seem to be an easy way to export the values of the settings from the app service's Configuration view (Microsoft: why not? There should be!).

Instead, you can get it from the app service's Kudu website (Development tools, Advanced tools, Go).  On the Kudu site's home page, there is an App Settings link under REST API which gives you a json file with the settings and their values.

This will take you to a url like this (with https://[yourappservicename].scm.azurewebsites.net being the address of the Kudu site):

https://[yourappservicename].scm.azurewebsites.net/api/settings

Note

For some reason, the list does not seem to include settings which are in the ConnectionStrings part of the app service's Configuration.  Why not? Again this seems odd, Microsoft.