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We present combined experimental and numerical work on light-matter interactions at nanometer length scales. We report numerical simulations of near-field infrared nanospectroscopy that consider detailed tip geometry and have no free parameters. Our results match published spectral shapes of amplitude and phase measurements even for strongly resonant surface phonon-polariton (SPhP) modes. They also verify published absolute scattering amplitudes. A unique, ultrabroadband light source enables near-field amplitude and phase acquisition into the far-infrared spectral range. This allowed us to discover a strong SPhP resonance in the polar dielectric SrTiO_{3} (STO) at an ∼24-μm wavelength of incident light.