Recombination and electron impact excitation of S14+ and S15+ ions was measured at the Stockholm refrigerated electron beam ion trap. The collision energy range was 1.4-3 keV, in which we covered the KLL, KLM, KLN, and KLO dielectronic recombination resonances resulting in S13+ and S14+ ions. The recombination rates were obtained by detecting the charge state distribution with a newly developed time-of-flight technique. Resonance energies and cross-sections calculated within the relativistic many-body perturbation theory for S15+ agree well with the experimental data. The temperature-dependent rate coefficients were extracted from the measured rates and compared with calculations from the literature used for studies of collisionally ionized astrophysical plasmas. Good agreement for S15+ was obtained, while the plasma rates for S14+ were 23% lower than the current published values. In addition to the time-of-flight spectra, the X-ray spectra, produced mainly by photo-recombination and excitation, were also collected. The combination of these two measurements allowed us to separate the photo-recombination and the excitation spectra, and the excitation rate coefficients for summed intensities with known fractions of S14+ and S15+ ions were extracted.