How to delete (localdb) database if the file is gone

In this situation, detach the database rather than trying to drop it. In SQL Management Studio, right-click on the database, select "Tasks" then "Detach".

All you need to do is to recreate the instance, tested with SQL 2012 ! just go in command prompt with admin rights and type:

//list the instancies
sqllocaldb i

//stop selected instance
sqllocaldb p "selected instance"

//delete
sqllocaldb d "selected instance"

//recreate or create new one 
sqllocaldb c "new instance"

I had the same problem. When designing DB using code first, I simply remove old DBs. It ends up with multiple deleted DB appearing in SQL Server Management Studio. Then when I try to query the DB, it becomes difficult to find the correct DB instance from amongst the deleted.

As IRM suggested, I tried to Detach those deleted DBs, and for some of them it works great!

However still I have several left. Then I tried "Take offline" on those DBs. Each time when I tried to take DB offline, the SQL Server Management Studio crashed. After SQL Server Management Studio restarted, the DB was gone. So try to do "take offline" if detach and delete don't work for you.