This usually means that a provider specified in one of your web.config connection strings is not installed on your machine. In my specific case the offender was this…

<add name="MyContext" 
    connectionString="Data Source=|DataDirectory|myDatabase.sdf"
    providerName="System.Data.SqlServerCe.4.0"/>

I needed to install SQL Server Compact 4.0
The same error will crop up for various other providers also.