Performance bugs are inefficiencies in software that waste computational resources without causing functional failures, making them particularly challenging to detect and fix. While recent advances in Software Engineering agents have shown promise in automated bug fixing, existing benchmarks primarily focus on functional correctness and fail to evaluate agents' abilities to identify and resolve non-functional issues like performance bugs. We introduce PerfBench, a benchmark comprising 81 real-world performance bug-fixing tasks from popular .NET repositories on GitHub. Unlike existing benchmarks that rely on pre-existing test suites, PerfBench features a novel evaluation harness that allows agents to generate their own performance benchmarks and validates fixes by comparing execution metrics collected for developer fix and agent fix. Each task in PerfBench is derived from actual developer fixes linked to performance-related issues, which are then verified by human experts, ensuring real-world relevance. Our evaluation reveals that current state-of-the-art coding agents struggle with performance optimization tasks, with baseline OpenHands agent achieving only a ~3% success rate on our benchmark. We develop OpenHands-Perf-Agent, which incorporates performance-aware tooling and instructions and achieves a ~20% success rate on the benchmark. We show that by ensuring the agent has proper instructions to benchmark its changes and tooling for benchmark output processing, we can improve the agent performance significantly, but room for improvement still remains. PerfBench provides a challenging test set for furthering the capabilities of agents in fixing performance issues.