Transformer-based, template-free SMILES-to-SMILES translation models for reaction prediction and single-step retrosynthesis are of interest to computer-aided synthesis planning systems, as they offer state-of-the-art accuracy. However, their slow inference speed limits their practical utility in such applications. To address this challenge, we propose speculative decoding with a simple chemically specific drafting strategy and apply it to the Molecular Transformer, an encoder-decoder transformer for conditional SMILES generation. Our approach achieves over 3X faster inference in reaction product prediction and single-step retrosynthesis with no loss in accuracy, increasing the potential of the transformer as the backbone of synthesis planning systems. To accelerate the simultaneous generation of multiple precursor SMILES for a given query SMILES in single-step retrosynthesis, we introduce Speculative Beam Search, a novel algorithm tackling the challenge of beam search acceleration with speculative decoding. Our methods aim to improve transformer-based models' scalability and industrial applicability in synthesis planning.