MAS research has investigated norms as a means to coordinate open multi-agent systems (MAS). This has spurred a strand of research on on-line norm synthesis algorithms for MASs. However, to the best of our knowledge, currently there is no computational framework to support the development and study of on-line norm synthesis. Here we present NORMLAB, a novel framework to support norm synthesis research, highlighting its important features. We also outline the operation of two novel on-line norm synthesis strategies, which significantly outperform the state of the art.