Weather forecasts from numerical weather prediction models play a central role in solar energy forecasting, where a cascade of physics-based models is used in a model chain approach to convert forecasts of solar irradiance to solar power production, using additional weather variables as auxiliary information. Ensemble weather forecasts aim to quantify uncertainty in the future development of the weather, and can be used to propagate this uncertainty through the model chain to generate probabilistic solar energy predictions. However, ensemble prediction systems are known to exhibit systematic errors, and thus require post-processing to obtain accurate and reliable probabilistic forecasts. The overarching aim of our study is to systematically evaluate different strategies to apply post-processing methods in model chain approaches: Not applying any post-processing at all; post-processing only the irradiance predictions before the conversion; post-processing only the solar power predictions obtained from the model chain; or applying post-processing in both steps. In a case study based on a benchmark dataset for the Jacumba solar plant in the U.S., we develop statistical and machine learning methods for post-processing ensemble predictions of global horizontal irradiance and solar power generation. Further, we propose a neural network-based model for direct solar power forecasting that bypasses the model chain. Our results indicate that post-processing substantially improves the solar power generation forecasts, in particular when post-processing is applied to the power predictions. The machine learning methods for post-processing yield slightly better probabilistic forecasts, and the direct forecasting approach performs comparable to the post-processing strategies.