High-solids anaerobic digestion (HS-AD) of the organic fraction of municipal solid waste (OFMSW) is operated at a total solid (TS) content ≥ 10% to enhance the waste treatment economy, though it might be associated to free ammonia (NH3) inhibition. This study aimed to calibrate and cross-validate a HS-AD model for homogenized reactors in order to assess the effects of high NH3 levels in HS-AD of OFMSW, but also to evaluate the suitability of the reversible non-competitive inhibition function to reproduce the effect of NH3 on the main acetogenic and methanogenic populations. The practical identifiability of structural/biochemical parameters (i.e. 35) and initial conditions (i.e. 32) was evaluated using batch experiments at different TS and/or inoculum-to-substrate ratios. Variance-based global sensitivity analysis and approximate Bayesian computation were used for parameter optimization. The experimental data in this study permitted to estimate up to 8 biochemical parameters, whereas the rest of parameters and biomass contents were poorly identifiable. The study also showed the relatively high levels of NH3 (i.e. up to 2.3 g N/L) and ionic strength (i.e. up to 0.9 M) when increasing TS in HS-AD of OFMSW. However, the NH3 non-competitive function was unable to capture the acetogenic/methanogenic inhibition. Therefore, the calibration emphasized the need for target-oriented experimental data to enhance the practical identifiability and the predictive capabilities of structured HS-AD models, but also the need for further testing the NH3 inhibition function used in these simulations.