I have recently upgraded to Visual Studio 2012 and SQL Server Management Studio 2012, however I cannot seem to see how to execute SQL scripts (created by Entity framework) on a SQL Server CE 4.0 database. With VS2010 + SSMS 2008 the Transact-SQL editor would ask for a connection and you could browse to the object, however this option is not available in SSMS 2012.
I have tried to execute the script via the Server Explorer -> New Query window, but I get parse errors. Any clues?
Microsoft got rid of that for SSMS 2012, and suggested to use the integrated tools in WebMatrix instead (from memory, can't find a link for that sorry).
As suggested in that Microsoft Answers post, however, you could use the SQL Server Compact Toolbox, it's pretty effective.
Try using the SQL Server Object Explorer instead of the Server Explorer. That should allow you to do what you wish.