This is easy to do, IF you have the right pieces.
For the connection string, you can use the JDBC connection string presented in the portal (see below).
For the JDBC driver, you need to be using Version 4. The reason is that earlier versions had problems with wildcard SSL certificates. You can download the driver at: http://www.microsoft.com/en-us/download/details.aspx?id=11774
We tested this using with Cold Fusion 10 installed in an Azure Virtual Machine.