InfiniBand is widely used for low-latency, high-throughput cluster computing. Saving the state of the InfiniBand network as part of distributed checkpointing has been a long-standing challenge for researchers. Because of a lack of a solution, typical MPI implementations have included custom checkpoint-restart services that "tear down" the network, checkpoint each node as if the node were a standalone computer, and then re-connect the network again. We present the first example of transparent, system-initiated checkpoint-restart that directly supports InfiniBand. The new approach is independent of any particular Linux kernel, thus simplifying the current practice of using a kernel-based module, such as BLCR. This direct approach results in checkpoints that are found to be faster than with the use of a checkpoint-restart service. The generality of this approach is shown not only by checkpointing an MPI computation, but also a native UPC computation (Berkeley Unified Parallel C), which does not use MPI. Scalability is shown by checkpointing 2,048 MPI processes across 128 nodes (with 16 cores per node). In addition, a cost-effective debugging approach is also enabled, in which a checkpoint image from an InfiniBand-based production cluster is copied to a local Ethernet-based cluster, where it can be restarted and an interactive debugger can be attached to it. This work is based on a plugin that extends the DMTCP (Distributed MultiThreaded CheckPointing) checkpoint-restart package.