We map a nanoindent in a silicon carbide (SiC) crystal by infrared (IR) scattering-type scanning near-field optical microscopy (s-SNOM) and confocal Raman microscopy and interpret the resulting images in terms of local residual stress-fields. By comparing near-field IR and confocal Raman images, we find that the stress-induced shifts of the longitudinal optical phonon-frequencies (LO) and the related shift of the phonon-polariton near-field resonance give rise to Raman and s-SNOM image contrasts, respectively. We apply single-frequency IR s-SNOM for nanoscale resolved imaging of local stress-fields and confocal Raman microscopy to obtain the complete spectral information about stress-induced shifts of the phonon frequencies at diffraction limited spatial resolution. The spatial extension of the local stress-field around the nanoindent agrees well between both techniques. Our results demonstrate that both methods ideally complement each other, allowing for the detailed analysis of stress-fields at e.g. material and grain boundaries, in Micro-Electro-Mechanical-Systems (MEMS), or in engineered nanostructures.