The convergence of Edge Computing (EC) and Machine Learning (ML), known as Edge Machine Learning (EML), has become a highly regarded research area by utilizing distributed network resources to perform joint training and inference in a cooperative manner. However, EML faces various challenges due to resource constraints, heterogeneous network environments, and diverse service requirements of different applications, which together affect the trustworthiness of EML in the eyes of its stakeholders. This survey provides a comprehensive summary of definitions, attributes, frameworks, techniques, and solutions for trustworthy EML. Specifically, we first emphasize the importance of trustworthy EML within the context of Sixth-Generation (6G) networks. We then discuss the necessity of trustworthiness from the perspective of challenges encountered during deployment and real-world application scenarios. Subsequently, we provide a preliminary definition of trustworthy EML and explore its key attributes. Following this, we introduce fundamental frameworks and enabling technologies for trustworthy EML systems, and provide an in-depth literature review of the latest solutions to enhance trustworthiness of EML. Finally, we discuss corresponding research challenges and open issues.