No Entity Framework provider found for the ADO.NET provider with invariant name ‘System.Data.SqlServerCe.4.0’

After installing the EntityFramework.SqlServerCompact nuget package, check that your app.config contains the following (as per @ErikEJ’s comment above):

<providers>
  <provider invariantName="System.Data.SqlClient" type="System.Data.Entity.SqlServer.SqlProviderServices, EntityFramework.SqlServer" />
  <provider invariantName="System.Data.SqlServerCe.4.0" type="System.Data.Entity.SqlServerCompact.SqlCeProviderServices, EntityFramework.SqlServerCompact" />
</providers>

(You can leave the line for SqlClient even though you don’t really need it.)