Adoption of zero-tillage practices with residue retention in field crops has been introduced as an alternative soil-management technique to counteract the resource degradation and high production costs derived from intensive tillage. In this sense, the biophysical models are valuable tools to evaluate and design the most suitable soil-management technique in view of future climate variability. The aim of this study was to use the ARMOSA process-based crop model to perform an assessment of tillage (T) and no-tillage (No-T) practices of durum-wheat-cropping systems in the Campania region (South of Italy) under current and future climate scenarios. First, the model was calibrated using measurements of soil water content at different depths, leaf area index, and aboveground biomass in the T and No-T treatments during the 2013–2014 season. Then, the model was further applied in the T and No-T treatments to future climate data for 2020–2100 that was generated by the COSMO-CLM model using the RCP4.5 and 8.5 paths. Results of the calibration depicted that the model can accurately simulate the soil-crop-related variables of both soil-management treatments, and thus can be applied to identify the most appropriate conservation agricultural practices in the durum-wheat system. The simulation of soil water content at different depths resulted in small relative root mean square errors (RRMSE < 15%) and an acceptable Pearson’s correlation coefficient (r > 0.51); and the goodness-of-fit indicators for simulated LAI and AGB resulted in acceptable RRMSE (RRMSE < 28%), and high r (r > 0.84) in both soil-management treatments. Future climate simulations showed that No-T management will deliver 10% more wheat yield than the T, with an annual average 0.31% year−1 increase of soil organic carbon, and an increase of 3.80% year−1 for N uptake, which can diminish the N leaching. These results suggest that No-T could be implemented as a more resilient management for farming system in view of climate uncertainty and scarcity of resources. Therefore, these findings support the potential of the ARMOSA model to evaluate the soil-crop response of the durum-wheat system under different management conditions and to design appropriate soil-management practices for current and future climate predictions.