Entity Framework 6 (EF6) code first migrations with models in separate project - ef-code-first

Question

Using EF6 code-first migrations, I am able to successfully save models and create new migrations for them. However, my DbContext class is in a Sharp.Data project, the actual (Sql CE) database lives under the Sharp.Server project bin folder, and my models live in a Sharp.Common project.
When I run add-migration -ProjectName Sharp.Data Migration3 (pointing to Sharp.Data as that is where the DbContext is), it successfully runs and identifies changes made to the models in the Sharp.Common project. However, when I run update-database -ProjectName Sharp.Data, it updates/creates/migrates/seeds a new database located under the bin folder of my Sharp.Data project, instead of Sharp.Server, where ultimately the application reads the data from.
Is there a way to do this? To have migrations generate/update a database that exists somewhere else besides its own project file? This may be a relic of using SQL CE, but it's my database of choice for various reasons.

Answer 1

You can pass extra parameters to update-database that allow to:
Specify a different connection string
Generate a SQL script that you can apply yourself to the target DB
Full syntax of Update-Database:
Update-Database [-SourceMigration <String>] [-TargetMigration <String>]
[-Script] [-Force] [-ProjectName <String>] [-StartUpProjectName <String>]
[-ConfigurationTypeName <String>] [-ConnectionStringName <String>]
[<CommonParameters>]
Update-Database [-SourceMigration <String>] [-TargetMigration <String>]
[-Script] [-Force] [-ProjectName <String>] [-StartUpProjectName <String>]
[-ConfigurationTypeName <String>] -ConnectionString <String>
-ConnectionProviderName <String> [<CommonParameters>]
To specify a connection string (which points to the correct folder in your project):
-StartUpProjectName and -ConnectionStringName, to specify a project that contains a .config file with a connection string with the provided name (1st syntax)
-ConnectionString, to specify directly the connection string (2nd syntax)
To create a SQL script that you can apply directly to the DB using other tool:
-SourceMigration: current migration in the destination DB -TargetMigration: migration to update to, and -Script: to generate a script taht you can apply by hand

Answer 2

#JotaBe's answer is correct. But to summise, you need to do the following:
add-migration "MigrationName" -ProjectName Sharp.Data -ConnectionString "ConnectionStringToYourTargetDatabaseHere"