This was setup awhile ago- https://www.siteground.com/tutorials/magento/magento_ssl.htm
The homepage is https and works fine. The sitemap still shows http and all of the navigation links still show http, there are other links as well that show http.
I have the setting selected as Use Secure URLs in the front end as yes. Is there another setting I should look at? Or is there another setting I am missing? Or do I need to go in and code everything that is not https?
Solution for you:
Go to : System -> Configuration -> General -> Web -> Unsecure -> Base URL setup it with your domain by https. So everything will be https. If there are still some pages show http that will be problem with hardcode with http, you can find them and replace with https.
Good luck !
Occasionally theme and extension developer forget that once HTTPS has been turned off all non-secure includes will cause browsers complain. This among other things apply to external font files ja jQuery libraries and whatnot. Make sure that those use that those will use either // as protocol or https://