Developing advanced surgical tools for minimally invasive procedures represents an activity of central importance to improving human health. A key challenge is in establishing biocompatible interfaces between the classes of semiconductor device and sensor technologies that might be most useful in this context and the soft, curvilinear surfaces of the body. This paper describes a solution based on materials that integrate directly with the thin elastic membranes of otherwise conventional balloon catheters, to provide diverse, multimodal functionality suitable for clinical use. As examples, we present sensors for measuring temperature, flow, tactile, optical and electrophysiological data, together with radiofrequency electrodes for controlled, local ablation of tissue. Use of such 'instrumented' balloon catheters in live animal models illustrates their operation, as well as their specific utility in cardiac ablation therapy. The same concepts can be applied to other substrates of interest, such as surgical gloves.