Sorry to hear about that, Ken. It happened to me too, about a year ago. The worst bit is going to the police to report the loss. If you are in the capital it is in that place behind the main police station on Av. Mexico. Chaotic to say the least. You make your report and pick up the certificate later in the day or the next day, depending on what time you made the initial report. Then you go to the JCE where they issue your replacement Cedula. Not sure about the residency card, I was in the process of getting my permanent residency so I just waited until I was issued the new one.
Hope this is helpful.
Chiri