Energy costs are an increasing part of the total cost of ownership of HPC systems. As HPC systems become increasingly energy proportional in an effort to reduce energy costs, interconnect links stand out for their inefficiency. Commodity interconnect links remain 'always-on', consuming full power even when no data is being transmitted. Although various techniques have been proposed towards energy-proportional interconnects, they are often too conservative or are not focused toward HPC. Aggressive techniques for interconnect energy savings are often not applied to HPC, in particular, because they may incur excessive performance overheads. Any energy-saving technique will only be adopted in HPC if there is no significant impact on performance, which is still the primary design objective. This paper explores interconnect energy proportionality from a performance perspective. We characterize HPC applications over on/off links and propose PerfBound, a technique that reduces link energy, subject to a bound on the application's performance degradation. We also propose PerfBoundRatio, which maintains the same performance bound across an entire hierarchical network. Finally, we propose PerfBoundPredict, which improves energy savings using an idle time prediction mechanism. Even when predictions are inaccurate, the performance degradation is still bounded. The techniques require no changes to the application and add no communication between nodes and/or switches. We evaluate our techniques using HPC traces from production supercomputers. Our results show that, configured with a 1% performance bound, 13 out of 15 applications are inside the bound, and average link energy savings are 60% for PerfBound and 68% for PerfBoundPredict.