Change your robots.txt file
Often the robots.txt file contains a pointer to your site's sitemap file. Make sure robots.txt is updated to point to the https location of the file.
Update your webmaster site properties
For example, in Google webmaster you need to add a new https property in addition to the http: property.
Update your analytics
Many analytics treat the https: address separate from the http: address. So make sure to update your analytics (such as Google or Bing analytics) to recognize the https address.