All great advice!
As a parent who has lossed a new born child. I would not wish this upon my worst enemy!
What ever you tell the parents make sure it is the truth and remember when you tell them be ready to comfort the parents the best you can. Never tell them that it is going to be okay or you know how they feel.
Tell them you are sorry for their loss, hug them if needed, ask if there is family members that you can contact for them. Let them grieve in their own way. They may scream at you,hit you, fall to the grownd, pass out, or not say anything. Just remember it is not your fault and that you and your partner did everything that could be done. Before leaving just make sure there is someone else there for the family as they should not be left alone after such a loss.
Just never lie!
Brian