We present numerical calculations, simulation results, and analytical considerations for the frequency-dependent dielectric constant of single-file water in narrow nanopores, described by a recently developed dipole lattice model. We find Debye relaxation over all length scales with relaxation times that strongly depend on pore length. This behavior is analyzed in terms of the dynamics of orientational defects leading to simple quantitative expressions for the static dielectric susceptibility and the relaxation time in the limits of short and long pores. Based on these formulas, we suggest how the predicted macroscopic order of nanopore water can be probed via dielectric spectroscopy and explain how the excitation energy, diffusion constant, and effective interaction of the defects that destroy the order can be extracted from such measurements.