Recent studies have explored the use of pre-trained embeddings for speech emotion recognition (SER), achieving comparable performance to conventional methods that rely on low-level knowledge-inspired acoustic features. These embeddings are often generated from models trained on large-scale speech datasets using self-supervised or weakly-supervised learning objectives. Despite the significant advancements made in SER through the use of pre-trained embeddings, there is a limited understanding of the trustworthiness of these methods, including privacy breaches, unfair performance, vulnerability to adversarial attacks, and computational cost, all of which may hinder the real-world deployment of these systems. In response, we introduce TrustSER, a general framework designed to evaluate the trustworthiness of SER systems using deep learning methods, with a focus on privacy, safety, fairness, and sustainability, offering unique insights into future research in the field of SER. Our code is publicly available under: https://github.com/usc-sail/trust-ser.