SQLite is apparently the most common option for WinRT applications. As you can see here , they made WinRT support a key feature of release 3.7.13. I am not too familiar with SQLite, but I think it could be (easy?) Used also for C #.
It seems that some people have successfully built SQLite processors for ARM, see here .
Given that ADO.NET and ODBC are not allowed in Windows Store applications, even if SQL Server Express can run on ARM, you will not be able to connect to it. We can safely assume that SQL Server Express and SQL Server Compact will not be available for Windows Store applications in the near future.