We distinguish two kinds of experimental activity: post-theory and exploratory. Posttheory experiment enjoys computer support that is well-aligned to the classical theory of computation. Exploratory experiment, in contrast, arguably demands a broader conception of computing. Empirical Modelling (EM) is proposed as a more appropriate conceptual framework in which to provide computational support for exploratory experiment. In the process, it promises to provide integrated computational support for both exploratory and post-theory experiment. We first sketch the motivation for EM and illustrate its potential for supporting experimentation, then briefly highlight the semantic challenge it poses and the philosophical implications.Advances in computing have led to a revolution in experimental practices in science. Much of this is focused on exploiting the power of computing technology to perform calculations and generate visualisations based on pre-existing scientific theories. Because such post-theory experiment can exploit a rationalisation of agency and state-change, it can be readily conceived within the framework of the classical theory of computation. In other contexts, computing technology is being used to support what can be construed as exploratory experiment, in a sense to be elaborated later. Though exploratory experimental activity is well-represented in computing practice-often in association with post-theory experiment-it is hard to accommodate within the accepted theoretical framework of computer science. We propose Empirical Modelling (EM) as an alternative conceptual framework for computing that is better adapted to the demands of exploratory experiment.The phrase "experimenting with computing" admits many interpretations. Two interpretations are topical in this paper. One refers to using computers in support of experimental activity, the other to innovative thinking associated with experiments in practical computing. Under both interpretations, the words 'experimenting' and 'computing' are being used in a broad sense-in contrast with the strict definitions of these activities that might be proposed in experimental science or computer science. Specifically, the term 'experimenting' is being used to refer quite generally to activities that involve taking an action whose effect is unknown, and the term 'computing' to the wide range of activities that exploit computer-related technology.The four principal sections of the paper: introduce the notions of exploratory and post-theory experiment; sketch key ideas from the philosophy of mathematics and science that motivate EM; illustrate the qualities of EM in support of exploratory experimental activity by means of a simple example; and briefly indicate some of the semantic and philosophical implications of adopting EM most relevant to theories and agency.