I've just uploaded my WCF REST based service to Azure.
When I try to use PUT or DELETE I get a 401, Unauthorized: Access is denied due to invalid credentials.
It runs fine in my local and Azure development environments
I've seen other posts referencing Certificates and Permissions.
401 Unauthorized with OData Update and Delete (PUT and DELETE verbs are enabled in IIS, by default)
http://goneale.com/2009/10/22/wcf-the-http-request-is-unauthorized-with-client-authentication-scheme-anonymous/ (doesn't apply because of Azure)
I'm running default settings