Management of agricultural waste is an important part of plantation operations. Not all wastes are suitable for composting or the process is simply inefficient and time-consuming. In their case, thermal treatment is acceptable, but it is necessary to optimize the process to minimize greenhouse gas emissions. This article investigates the feasibility of constructing artificial neural networks (ANNs) to predict feedstock and emission parameters from the combustion of vineyard biomass. In order to maximize accuracy while avoiding overfitting of the ANN, a novel dual-ANN system was proposed. It consisted of two cascade-forward ANNs trained on independent data, each with three hidden layers. A benchmark showed that the final networks had a relative error in the range of 0.81–2.83%, and the resulting dual-ANN up to a maximum of 2.09%. Based on the ANN, it was possible to make recommendations on the parameters of the feedstock that would be suitable for obtaining bioenergy. It was noted that the best calorific values are shown by waste from plants with an intermediate amount, distribution, and mass of leaves, with relatively low average leaf area. Emissivity reduction, however, requires significantly different conditions. Preference is given to waste from plants that have high amounts of leaves but are spread over many stems — that is, plants that are highly shrubby during the growing season. This proves that it is not possible to formulate universal recommendations that are both energy- and carbon-beneficial, but outlines a clear direction where consensus should be sought, depending on the goals adopted.