Phil Parkin (9/25/2016)

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Well, you can at least connect to it from SSDT.

Choose Tools/SQL Server/New Query and then expand the 'local' node to select the connection you are interested in.

When I did this and ran

SELECT @@SERVERNAME

I got some nonsense back (machine name\LOCALDB#90ACA499).

So I tried connecting to that in SSMS, but the connection was unsuccessful (received a generic 'cannot connect to ...' error).