Https - should I do change of address on WMT
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We have added a SSL cert to our site - Should I submit change of address on WMT and submit a new sitemap from the http?
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Have you setup your https version of the site in webmaster tools as a separate site, if not I would and then I would submit a https sitemap on this profile.
I would also 301 redirect the http to https across the site - you may find this previous question useful - http://moz.com/community/q/best-method-of-redirecting-http-to-https-on-homepage