One great advantage of using Azure Websites is that I can get secure HTTP (HTTPS) without doing nothing: I simply type https://xyz.azurewebsites.net and it works. I don't have to worry about certificates because I use the subdomain that Azure gives me (in the example it would be xyz)
So, what I usually do is that people come by through some registered domain I have, eg. http://www.my-application-homepage.com, and there, if they want to use my application, I redirect them to the subdomain at azurewebsites.net, using HTTPS.
Now, having said that:
I'm in need of upgrading to Azure Cloud Services or Azure Virtual Machines, because these have capabilities that Azure Websites don't . These two also offer a free subdomain: xyz.cloudapp.net, but my question is: will I get HTTPS there too? and how?
I searched in google for some cloudapp examples and what I tested was the following:
1) Connect through HTTP (ie. type http://xyz.cloudapp.net). Result: worked
2) Connect through HTTPS (ie. type https://xyz.cloudapp.net). Result: didn't work (chrome gave ERR_CONNECTION_TIMED_OUT)
No. HTTPS is not offered for .cloudapp.net domain as of today. Also since you don't own .cloudapp.net domain, I don't think you can buy a SSL certificate for that. If you want you could create a self-signed certificate and use that.