The reuse of historical clinical trial data has significant potential to accelerate medical research and drug development. However, interoperability challenges, particularly with missing medical codes, hinders effective data integration across studies. While Large Language Models (LLMs) offer a promising solution for automated coding without labeled data, current approaches face challenges on complex coding tasks. We introduce ALIGN, a novel compositional LLM-based system for automated, zero-shot medical coding. ALIGN follows a three-step process: (1) diverse candidate code generation; (2) self-evaluation of codes and (3) confidence scoring and uncertainty estimation enabling human deferral to ensure reliability. We evaluate ALIGN on harmonizing medication terms into Anatomical Therapeutic Chemical (ATC) and medical history terms into Medical Dictionary for Regulatory Activities (MedDRA) codes extracted from 22 immunology trials. ALIGN outperformed the LLM baselines, while also providing capabilities for trustworthy deployment. For MedDRA coding, ALIGN achieved high accuracy across all levels, matching RAG and excelling at the most specific levels (87-90% for HLGT). For ATC coding, ALIGN demonstrated superior performance, particularly at lower hierarchy levels (ATC Level 4), with 72-73% overall accuracy and 86-89% accuracy for common medications, outperforming baselines by 7-22%. ALIGN's uncertainty-based deferral improved accuracy by 17% to 90% accuracy with 30% deferral, notably enhancing performance on uncommon medications. ALIGN achieves this cost-efficiently at \$0.0007 and \$0.02 per code for GPT-4o-mini and GPT-4o, reducing barriers to clinical adoption. ALIGN advances automated medical coding for clinical trial data, contributing to enhanced data interoperability and reusability, positioning it as a promising tool to improve clinical research and accelerate drug development.