One great advantage of using Azure Websites is that I can get secure HTTP (HTTPS) without doing nothing: I simply type https://xyz.azurewebsites.
** Update: This method is not valid as well, we got the certificate revoked after one week using it **
We use this approach for staging/dev servers:
If you don't want to use a self-signed certificate, one option is to purchase a cheap SSL certificate, e.g.:
https://www.ssls.com/comodo-ssl-certificates/positivessl.html
Then once you need to approve it you have to ask support to change the approver validation process: instead of sending an email to a admin@mydomain.cloudapp.net you can ask to change the validation process to placing a given file with a given file in the root of your website (you have to ask in the support / chat room about that option).
More info:
https://support.comodo.com/index.php?/Default/Knowledgebase/Article/View/791/16/alternative-methods-of-domain-control-validation-dcv