Context: Speech Emotion Recognition (SER) is a valuable technology that identifies human emotions from spoken language, enabling the development of context-aware and personalized intelligent systems. To protect user privacy, Federated Learning (FL) has been introduced, enabling local training of models on user devices. However, FL raises concerns about the potential exposure of sensitive information from local model parameters, which is especially critical in applications like SER that involve personal voice data. Local Differential Privacy (LDP) has prevented privacy leaks in image and video data. However, it encounters notable accuracy degradation when applied to speech data, especially in the presence of high noise levels. In this paper, we propose an approach called LDP-FL with CSS, which combines LDP with a novel client selection strategy (CSS). By leveraging CSS, we aim to improve the representatives of updates and mitigate the adverse effects of noise on SER accuracy while ensuring client privacy through LDP. Furthermore, we conducted model inversion attacks to evaluate the robustness of LDP-FL in preserving privacy. These attacks involved an adversary attempting to reconstruct individuals' voice samples using the output labels provided by the SER model. The evaluation results reveal that LDP-FL with CSS achieved an accuracy of 65-70%, which is 4% lower than the initial SER model accuracy. Furthermore, LDP-FL demonstrated exceptional resilience against model inversion attacks, outperforming the non-LDP method by a factor of 10. Overall, our analysis emphasizes the importance of achieving a balance between privacy and accuracy in accordance with the requirements of the SER application.