In modern computers, non-performance metrics such as energy consumption have become increasingly important, requiring tradeoff with performance. A recent work has proposed performance-guaranteed energy management, but it is designed specifically for sequential applications and cannot be used to a large class of multithreaded applications running on high end computers and data servers. To address the above problem, this paper makes the first attempt to provide performance-guaranteed energy management for multithreaded applications on multiprocessor architectures. We first conduct a comprehensive study on the effects of energy adaptation on thread synchronizations and show that a multithreaded application suffers from not only local slowdowns due to energy adaptation, but also significant slowdowns propagated from other threads because of synchronization. Based on these findings, we design three Synchronization-Aware (SA) algorithms, LWT (Lock Waiting Time-based), CSL (Critical Section Length-based) and ODP (Operation Delay Propagation-based) algorithms, to estimate the energy adaptation-induced slowdowns on each thread. The local slowdowns are then combined across multiple threads via three aggregation methods (MAX, AVG and SUM) to estimate the overall application slowdown. We evaluate our methods using a large multithreaded commercial application, IBM DB2 with industrial-strength online transaction processing (OLTP) workloads, and six SPLASH parallel scientific applications. Our experimental results show that LWT combined with the MAX aggregation method not only controls the performance slow down within the specified limits but also conserves the most energy.