  We study the degree of reliability of extrapolation of complex
electromagnetic permittivity functions based on their analyticity properties.
Given two analytic functions, representing extrapolants of the same
experimental data, we examine how much they can differ at an extrapolation
point outside of the experimentally accessible frequency band. We give a sharp
upper bound on the worst case extrapolation error, in terms of a solution of an
integral equation of Fredholm type. We conjecture and give numerical evidence
that this bound exhibits a power law precision deterioration as one moves
further away from the frequency band containing measurement data.
