Surface-phonon polaritons (SPhPs) are attractive alternatives to far-infrared plasmonics for sub-diffractional confinement of light. Localized SPhP resonances in semiconductor nanoresonators are very narrow, but that linewidth and the limited extent of the Reststrahlen band inherently limit spectral coverage. To address this limitation, we report active tuning of SPhP resonances in InP and 4H-SiC by photoinjecting free carriers into the nanoresonators, taking advantage of the coupling between the carrier plasma and optical phonons to blue-shift SPhP resonances. We demonstrate state-of-the-art tuning figures of merit upon continuous-wave (CW) excitation (in InP) or pulsed excitation (in 4H-SiC). Lifetime effects cause the tuning to saturate in InP, and carrier-redistribution leads to rapid (<50 ps) recovery of the tuning in 4H-SiC. This work opens the path toward actively tuned nanophotonic devices, such as modulators and beacons, in the infrared and identifies important implications of coupling between electronic and photonic excitations.