Large Language Models (LLMs) demonstrate strong potential across a variety of tasks in communications and networking due to their advanced reasoning capabilities. However, because different LLMs have different model structures and are trained using distinct corpora and methods, they may offer varying optimization strategies for the same network issues. Moreover, the limitations of an individual LLM's training data, aggravated by the potential maliciousness of its hosting device, can result in responses with low confidence or even bias. To address these challenges, we propose a blockchain-enabled collaborative framework that connects multiple LLMs into a Trustworthy Multi-LLM Network (MultiLLMN). This architecture enables the cooperative evaluation and selection of the most reliable and high-quality responses to complex network optimization problems. Specifically, we begin by reviewing related work and highlighting the limitations of existing LLMs in collaboration and trust, emphasizing the need for trustworthiness in LLM-based systems. We then introduce the workflow and design of the proposed Trustworthy MultiLLMN framework. Given the severity of False Base Station (FBS) attacks in B5G and 6G communication systems and the difficulty of addressing such threats through traditional modeling techniques, we present FBS defense as a case study to empirically validate the effectiveness of our approach. Finally, we outline promising future research directions in this emerging area.