By the end of 2023, renewable sources covered 63.4% of the total electric-power demand of Chile, and, in line with the global trend, photovoltaic (PV) power showed the most dynamic increase. Although Chile's Atacama Desert is considered to be the sunniest place on Earth, PV power production, even in this area, can be highly volatile. Successful integration of PV energy into the country's power grid requires accurate short-term PV power forecasts, which can be obtained from predictions of solar irradiance and related weather quantities. Nowadays, in weather forecasting, the state-of-the-art approach is the use of ensemble forecasts based on multiple runs of numerical weather prediction models. However, ensemble forecasts still tend to be uncalibrated or biased, thus requiring some form of post-processing. The present work investigates probabilistic forecasts of solar irradiance for regions III and IV in Chile. For this reason, eight-member short-term ensemble forecasts of solar irradiance for the calendar year 2021 are generated using the Weather Research and Forecasting (WRF) model; these are then calibrated using the benchmark ensemble model output statistics (EMOS) method based on a censored Gaussian law and its machine-learning-based distributional regression network (DRN) counterpart. Furthermore, we also propose a neural-network-based post-processing method, resulting in improved eight-member ensemble predictions. All forecasts are evaluated against station observations for 30 locations in the study area, and the skill of post-processed predictions is compared to the raw WRF ensemble. Our case study confirms that all studied post-processing methods substantially improve both the calibration of probabilistic forecasts and the accuracy of point forecasts. Among the methods tested, the corrected ensemble exhibits the best overall performance. Additionally, the DRN model generally outperforms the corresponding EMOS approach.