Browser-using agents (BUAs) are an emerging class of autonomous agents that interact with web browsers in human-like ways, including clicking, scrolling, filling forms, and navigating across pages. While these agents help automate repetitive online tasks, they are vulnerable to prompt injection attacks that can trick an agent into performing undesired actions, such as leaking private information or issuing state-changing requests. We propose ceLLMate, a browser-level sandboxing framework that restricts the agent's ambient authority and reduces the blast radius of prompt injections. We address two fundamental challenges: (1) The semantic gap challenge in policy enforcement arises because the agent operates through low-level UI observations and manipulations; however, writing and enforcing policies directly over UI-level events is brittle and error-prone. To address this challenge, we introduce an agent sitemap that maps low-level browser behaviors to high-level semantic actions. (2) Policy prediction in BUAs is the norm rather than the exception. BUAs have no app developer to pre-declare sandboxing policies, and thus, ceLLMate pairs website-authored mandatory policies with an automated policy-prediction layer that adapts and instantiates these policies from the user's natural-language task. We implement ceLLMate as an agent-agnostic browser extension and demonstrate how it enables sandboxing policies that effectively block various types of prompt injection attacks with negligible overhead.