Interpolate NA values

The proper way to do this statistically and still get valid confidence intervals is to use Multiple Imputation. See Rubin's classic book, and there's an excellent R package for this (mi).

Using the zoo package:

library(zoo)
Cz <- zoo(C)
index(Cz) <- Cz[,1]
Cz_approx <- na.approx(Cz)