Concurrency control (CC) algorithms must trade off strictness for performance. Serializable CC schemes generally pay higher cost to prevent anomalies, both in runtime overhead and in efforts wasted by aborting transactions. We propose the serial safety net (SSN), a serializability-enforcing certifier which can be applied with minimal overhead on top of various CC schemes that offer higher performance but admit anomalies, such as snapshot isolation and read committed. The underlying CC retains control of scheduling and transactional accesses, while SSN tracks the resulting dependencies. At commit time, SSN performs an efficient validation test by examining only direct dependencies of the committing transaction to determine whether it can commit safely or must abort to avoid a potential dependency cycle. SSN performs robustly for various workloads. It maintains the characteristics of the underlying CC without biasing toward certain types of transactions, though the underlying CC might. Besides traditional OLTP workloads, SSN also allows efficient handling of heterogeneous workloads with long, read-mostly transactions. SSN can avoid tracking the majority of reads (thus reducing the overhead of serializability certification) and still produce serializable executions with little overhead. The dependency tracking and validation tests can be done efficiently, fully parallel and latch-free, for multi-version systems on modern hardware with substantial core count and large main memory. We demonstrate the efficiency, accuracy and robustness of SSN using extensive simulations and an implementation that overlays snapshot isolation in ERMIA, a memory-optimized OLTP engine that is capable of running different CC schemes. Evaluation results confirm that SSN is a promising approach to serializability with robust performance and low overhead for various workloads.