Frontier Large language models (LLMs) like ChatGPT and Gemini can decipher cryptic compiler errors for novice programmers, but their computational scale, cost, and tendency to over-assist make them problematic for widespread pedagogical adoption. This work demonstrates that smaller, specialised language models, enhanced via Supervised Fine-Tuning (SFT), present a more viable alternative for educational tools. We utilise a new dataset of 40,000 C compiler error explanations, derived from real introductory programming (CS1/2) student-generated programming errors, which we used to fine-tune three open-source models: Qwen3-4B, Llama-3.1-8B, and Qwen3-32B. We performed a dual evaluation, combining expert human reviews with a large-scale automated analysis of 8,000 responses using a validated LLM-as-judge ensemble. Our results show that SFT significantly boosts the pedagogical quality of smaller models, achieving performance comparable to much larger models. We analyse the trade-offs between model size and quality, confirming that fine-tuning compact, efficient models on high-quality, domain-specific data is a potent strategy for creating specialised models to drive educational tools. We provide a replicable methodology to foster broader access to generative AI capabilities in educational contexts.