Neologism-aware machine translation aims to translate source sentences containing neologisms into target languages. This field remains underexplored compared with general machine translation (MT). In this paper, we propose an agentic framework, NeoAMT, for neologism-aware machine translation equipped with a Wiktionary-based search toolkit. Specifically, we first construct a dedicated dataset for neologism-aware machine translation and build a search toolkit grounded in Wiktionary. The dataset covers 16 languages and 75 translation directions in total, derived from approximately 10 million records of an English Wiktionary dump. The retrieval corpus of the search toolkit is also constructed from around 3 million cleaned records of the same dump. We then leverage the dataset and toolkit to train a translation agent via reinforcement learning (RL) and to evaluate the accuracy of neologism-aware machine translation. Furthermore, we propose an RL training framework featuring a novel reward design and an adaptive rollout generation strategy that exploits translation difficulty to further improve the translation quality of translation agents using our search toolkit.