Complex electromagnetic permittivity functions are functions of frequency that have analytic extension into the upper half-plane. Their positive imaginary parts describe the absorption of EM radiation of a given frequency by materials, while their real parts describe the refractive properties. This function can be measured in a band of frequencies, and one wants to use its analyticity to extrapolate to a wider band of frequencies. A fundamental question is how reliable such extrapolation algorithms can possibly be. In a joint work with Narek Hovsepyan we have been able to recast the problem in terms of stability of analytic continuation of Hardy functions. In another joint work with Narek the latter problem is reduced to a solution of a linear integral equation of Fredholm type, which can be solved numerically, leading to a quantification of uncertainty of any extrapolation procedure.