If you are using object contex data model (with EDMX file), during its creation you might want to specify the connection string inside your config file.
The connect
Turns out there are two ways.
I could parse the entity connection string via the EntityConnectionStringBuilder:
string entityConnectionString = ConfigurationManager.ConnectionStrings["MyDbEntities"].ConnectionString;
string providerConnectionString = new EntityConnectionStringBuilder(entityConnectionString).ProviderConnectionString;
...or if I have the specific model instance available, I can get it from here.
((System.Data.EntityClient.EntityConnection)ModelInstance.Connection).StoreConnection.ConnectionString;