Here are the three web pages on which we found the answer. The most difficult part was setting up static ports for SQLEXPRESS.
Provisioning a SQL Server Virtual Machine on Windows Azure. These initial instructions provided 25% of the answer.
How to Troubleshoot Connecting to the SQL Server Database Engine. Reading this carefully provided another 50% of the answer.
How to configure SQL server to listen on different ports on different IP addresses?. This enabled setting up static ports for named instances (eg SQLEXPRESS.) It took us the final 25% of the way to the answer.