Amazon Web Services (AWS) are offering an instance of SQL Server Express for free. This is a great way to try out the service and see if it works for your scenario.
After you sign up (credit card required) you are able to provision an instance quite quickly. Note my highlighted Red box that contains the endpoint of the SQL Server instance.
Then all you have to do is setup the security group and specify the IP of the machine attempting to reach the instance. Amazon makes a suggestion based on the machine making the request.
You can now connect to your instance from SQL Server Management Studio. (Note that the instance is SQL Server 2008 R2)
You can then use it as any other SQL Server instance.