Testing web forms is an essential activity for ensuring the quality of web applications. It typically involves evaluating the interactions between users and forms. Automated test-case generation remains a challenge for web-form testing: Due to the complex, multi-level structure of web pages, it can be difficult to automatically capture their inherent contextual information for inclusion in the tests. Large Language Models (LLMs) have shown great potential for contextual text generation. This motivated us to explore how they could generate automated tests for web forms, making use of the contextual information within form elements. To the best of our knowledge, no comparative study examining different LLMs has yet been reported for web-form-test generation. To address this gap in the literature, we conducted a comprehensive empirical study investigating the effectiveness of 11 LLMs on 146 web forms from 30 open-source Java web applications. In addition, we propose three HTML-structure-pruning methods to extract key contextual information. The experimental results show that different LLMs can achieve different testing effectiveness. Compared with GPT-4, the other LLMs had difficulty generating appropriate tests for the web forms: Their successfully-submitted rates (SSRs) decreased by 9.10% to 74.15%. Our findings also show that, for all LLMs, when the designed prompts include complete and clear contextual information about the web forms, more effective web-form tests were generated. Specifically, when using Parser-Processed HTML for Task Prompt (PH-P), the SSR averaged 70.63%, higher than the 60.21% for Raw HTML for Task Prompt (RH-P) and 50.27% for LLM-Processed HTML for Task Prompt (LH-P). Finally, this paper also highlights strategies for selecting LLMs based on performance metrics, and for optimizing the prompt design to improve the quality of the web-form tests.