The growing demand for real-time neural network inference has heightened the need for hardware capable of efficiently executing the Softmax function, which relies on exponentials and divisions and is costly, numerically sensitive, and resource-intensive in hardware implementations. This work explores two hardware design approaches—manual Register-Transfer Level design and High-Level Synthesis design—each incorporating distinct approximation strategies to overcome these challenges. By evaluating their cost, performance, and accuracy trade-offs, the study aims to identify the most effective design alternatives and provide practical guidelines for deploying Softmax-based deep learning models on FPGAs in energy and latency-constrained embedded environments.