This paper formalizes a methodology based on Kriging, a technique developped by geostatisticians, for estimating derivatives and integrals of signals that are only known via possibly irregularly spaced and noisy observations. This finds direct applications, e.g., in system identification when differential algebra is used to express parameters as nonlinear functions of the inputs and outputs and their derivatives. The procedure is quite simple to implement, and allows confidence intervals on the predicted values to be derived.