Next-generation non-volatile memories (NVMs) promise DRAM-like performance, persistence, and high density. They can attach directly to processors to form non-volatile main memory (NVMM) and offer the opportunity to build very low-latency storage systems. These high-performance storage systems would be especially useful in large-scale data center environments where reliability and availability are critical. However, providing reliability and availability to NVMM is challenging, since the latency of data replication can overwhelm the low latency that NVMM should provide.We propose Mojim, a system that provides the reliability and availability that large-scale storage systems require, while preserving the performance of NVMM. Mojim achieves these goals by using a two-tier architecture in which the primary tier contains a mirrored pair of nodes and the secondary tier contains one or more secondary backup nodes with weakly consistent copies of data. Mojim uses highlyoptimized replication protocols, software, and networking stacks to minimize replication costs and expose as much of NVMM's performance as possible. We evaluate Mojim using raw DRAM as a proxy for NVMM and using an industrial NVMM emulation system. We find that Mojim provides replicated NVMM with similar or even better performance than un-replicated NVMM (reducing latency by 27% to 63% and delivering between 0.4 to 2.7× the throughput). We demonstrate that replacing MongoDB's built-in replication system with Mojim improves MongoDB's performance by 3.4 to 4×.