The paper presents a concept of an air pollution monitoring system with prediction abilities, based on wireless smart sensors, that takes into account local conditions (microclimate) prevailing in particular areas of the city. In most cases reported in the literature, artificial neural networks (ANNs) are used to predict future pollution levels. In existing solutions of this type, ANNs are trained with generalized datasets common for larger areas, e.g., cities. Our investigations show, however, that conditions may strongly differ even between particular streets in the city, which may impact prediction quality. This results from varying density of urban development, different levels of insolation, airiness, amounts of greenery, etc. As a result, with similar values of ANN input signals, such as current pollution levels, temperature, pressure, etc., the results of the prediction may differ significantly from reality. For this reason, we propose an innovative solution, in which particular sensors are equipped with miniaturized low-power ANNs, trained with datasets gathered directly from their closest environment, without a need for the obtaining of such data from a base station. This may simplify the installation and maintenance process of a network of such sensors. In a further part of this work, we dealt with solutions that enable the reduction of the computational complexity of ANNs in the case of their implementation on specialized integrated circuits. We propose replacing the most complex mathematical operations used in the learning algorithm with simpler solutions. A prototype chip containing the main blocks of such an ANN was also designed.