Background: Medical coding structures healthcare data for research, quality monitoring, and policy. This study assesses the potential of large language models (LLMs) to assign ICPC-2 codes using the output of a domain-specific search engine. Methods: A dataset of 437 Brazilian Portuguese clinical expressions, each annotated with ICPC-2 codes, was used. A semantic search engine (OpenAI's text-embedding-3-large) retrieved candidates from 73,563 labeled concepts. Thirty-three LLMs were prompted with each query and retrieved results to select the best-matching ICPC-2 code. Performance was evaluated using F1-score, along with token usage, cost, response time, and format adherence. Results: Twenty-eight models achieved F1-score > 0.8; ten exceeded 0.85. Top performers included gpt-4.5-preview, o3, and gemini-2.5-pro. Retriever optimization can improve performance by up to 4 points. Most models returned valid codes in the expected format, with reduced hallucinations. Smaller models (<3B) struggled with formatting and input length. Conclusions: LLMs show strong potential for automating ICPC-2 coding, even without fine-tuning. This work offers a benchmark and highlights challenges, but findings are limited by dataset scope and setup. Broader, multilingual, end-to-end evaluations are needed for clinical validation.