Searching and detecting the task-relevant parts of plants is important to automate harvesting and de-leafing of tomato plants using robots. This is challenging due to high levels of occlusion in tomato plants. Active vision is a promising approach in which the robot strategically plans its camera viewpoints to overcome occlusion and improve perception accuracy. However, current active-vision algorithms cannot differentiate between relevant and irrelevant plant parts and spend time on perceiving irrelevant plant parts. This work proposed a semantics-aware active-vision strategy that uses semantic information to identify the relevant plant parts and prioritise them during view planning. The proposed strategy was evaluated on the task of searching and detecting the relevant plant parts using simulation and real-world experiments. In simulation experiments, the semantics-aware strategy proposed could search and detect 81.8% of the relevant plant parts using nine viewpoints. It was significantly faster and detected more plant parts than predefined, random, and volumetric active-vision strategies that do not use semantic information. The strategy proposed was also robust to uncertainty in plant and plant-part positions, plant complexity, and different viewpoint-sampling strategies. In real-world experiments, the semantics-aware strategy could search and detect 82.7% of the relevant plant parts using seven viewpoints, under complex greenhouse conditions with natural variation and occlusion, natural illumination, sensor noise, and uncertainty in camera poses. The results of this work clearly indicate the advantage of using semantics-aware active vision for targeted perception of plant parts and its applicability in the real world. It can significantly improve the efficiency of automated harvesting and de-leafing in tomato crop production.