Well, if radar fails, then flights make position reports over navigation landmarks and the controllers keep track of who's where based on their reports.
If an airplane's radios go out, there's a procedure for that.
I don't know what the procedure is for a whole Center's radios going out, except for diverting incoming flights before they reach the affected area, and stopping other flights from departing.
Thanks for the clarification. After I rush posted, I realized the error of my comment. They're not backups for each other, but seperate tools which have their own backups.