Today, blockchain ledgers utilize concurrent deterministic execution schemes to scale up. However, ordering fairness is not preserved in these schemes: although they ensure all replicas achieve the same serial order, this order does not always align with the fair, consensus-established order when executing smart contracts with runtime-determined accesses. To preserve ordering fairness, an intuitive method is to concurrently execute transactions and re-execute any order-violating ones. This in turn increases unforeseen conflicts, leading to scaling bottlenecks caused by numerous costly aborts under contention. To address these issues, we propose Spectrum, a novel deterministic execution scheme for smart contract execution on blockchain ledgers. Spectrum preserves the consensus-established serial order (so-called strict determinism) with high performance. Specifically, we leverage a speculative deterministic concurrency control to execute transactions in speculation and enforce an agreed-upon serial order by aborting and re-executing any mis-speculated ones. To overcome the scaling bottleneck, we present two key optimizations based on speculative processing: operation-level rollback and predictive scheduling, for reducing both the overhead and the number of mis-speculations. We evaluate Spectrum by executing EVM-based smart contracts on popular benchmarks, showing that it realizes fair smart contract execution by preserving ordering fairness and outperforms competitive schemes in contended workloads by 1.4x to 4.1x.