Given a SQL Connection String is in the clipboard:

Server=tcp:my-sql-azure-sql-server-name.database.windows.net,1433;Database=my-initial-catalog;User ID=user@my-sql-azure-sql-server-name;Password=ALRh2AxHV6f8;Trusted_Connection=False;Encrypt=True;Connection Timeout=30;

When the "Server" property of the connection string or equivalent ends with ".database.windows.net,1433" then the assumption that this database server is a SQL Azure connection string and automatically select the "SQL Azure" radio button at the top of the "LINQPad Connection" dialog box.