Azure now allows you to get a free certificate for your website running as an app service.
This feature is currently under preview, expect some of the screenshots to be different to what you see in the portal...
Get your certificate here...
Open the Azure Portal and select App Services.
Select the app service you want to protect with a certificate.
Then open TLS/SSL Settings
Select the Private Key Certificate tab and click on Create App Service Managed Certificate.
Next, select your web site domain, and click Create.
This will add the certificate.
That's it! Nice and simple!