Measurements of electron-impact excitation and recombination rate coefficients of highly charged Si and S ions at the Stockholm electron beam ion trap are reported. The experimental method was a combination of photon detection from the trapped ions during probing and subsequently extraction and time-of-flight (TOF) charge analysis of these ions. The TOF technique allows to measure recombination rate coefficients separately for every charge state, and together with the photon spectra of these ions also the excitation rate coefficients. In this paper, we present more details of the experimental procedure and summarize the experimental results in comparison with two different state-of-the-art calculations of recombination and excitation rates for Si¹⁰⁺–Si¹³⁺ and S¹²⁺–S¹⁵⁺ ions. One of these uses a relativistic configuration interaction approach (flexible atomic code) and the other is a relativistic many-body perturbation theory. A good to excellent agreement with both of them is found in energy and resonance strength for the investigated ions.