Human oversight of large language models (LLMs) and artificial intelligence (AI) agents increasingly depends on their reports. Claims that conflict with a system's own judgments can conceal failures, prevent timely intervention, and contribute to severe harm. Greater autonomy makes faithful reporting increasingly important for maintaining human control. In this vision paper, we propose honesty testing of LLMs and AI agents as a new research area in software engineering. Building on existing honesty evaluations, our goal is to make faithful reporting a software quality requirement that developers can specify, test, and maintain. We define honesty bugs as behavioural defects in which an LLM or AI agent, when required to communicate faithfully, makes an explicit claim that conflicts with its own judgment at the time of reporting. We present an initial framework covering LLM-level testing under controlled inputs and agent-level testing of complete systems. The framework connects these levels to testing workflows and oracle evidence. We identify research directions in benchmarks, model and harness analysis, oracle construction, and lifecycle testing to support effective oversight alongside task correctness.

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