I found a user guide for the Standardized Technology Evaluation Process (STEP) developed by MITRE . This guide provides a methodology for evaluation teams to conduct technology evaluations that are efficient, repeatable, and as objective as possible. The guide is divided into three phases: Scoping and Test Strategy, Test Preparation, and Testing, Results, and Final Report. Each phase has a set of actions that need to be performed to ensure the evaluation is successful .
Additionally, I found an article on Software Advice that outlines a five-step process for evaluating new software. The process includes conducting a needs analysis, identifying must-have features, selecting a vendor, testing the software, and making the final decision .