Cognitive science and cognitive psychology have long used creativity tests to measure and investigate the relationships between creativity, creative problem solving and other cognitive abilities. Implementing cognitive systems that can model and/or solve creativity tests can shed light on the cognitive process, and presents the possibility of building much more precise creativity measuring tools. This paper describes four cognitive AI systems related to the Remote Associates Test (RAT) and their contributions to creativity science. comRAT-C is a system that solves the RAT, correlating with human performance. comRAT-G reverse engineers this process to generate RAT queries with a high degree of parameter control. fRAT generates functional RAT queries, resurrecting a theoretical concept proposed by researchers many decades ago. The visual RAT takes advantage of the formal conceptualization necessary for computational implementation, to expand the RAT to the visual domain. All the cognitive systems and generated RAT queries have been successfully validated with human participants and have contributed in improving creativity modeling and measuring tools.