Generative large language models (LLMs) are a promising alternative topre-trained language models for entity matching due to their high zero-shotperformance and ability to generalize to unseen entities. Existing research onusing LLMs for entity matching has focused on prompt engineering and in-contextlearning. This paper explores the potential of fine-tuning LLMs for entitymatching. We analyze fine-tuning along two dimensions: 1) the representation oftraining examples, where we experiment with adding different types ofLLM-generated explanations to the training set, and 2) the selection andgeneration of training examples using LLMs. In addition to the matchingperformance on the source dataset, we investigate how fine-tuning affects themodels ability to generalize to other in-domain datasets as well as acrosstopical domains. Our experiments show that fine-tuning significantly improvesthe performance of the smaller models while the results for the larger modelsare mixed. Fine-tuning also improves the generalization to in-domain datasetswhile hurting cross-domain transfer. We show that adding structuredexplanations to the training set has a positive impact on the performance ofthree out of four LLMs, while the proposed example selection and generationmethods, only improve the performance of Llama 3.1 8B while decreasing theperformance of GPT-4o-mini.