"In dynamical systems, invariant objects can be computed efficiently via numerical continuation of solutions to a suitably defined boundary-value problem. This presentation will start with a brief overview of the basic ideas behind the numerical continuation method, and some examples of typical applications. The main focus of the presentation is determining how oscillating models shift in phase in response to stimuli. I will present numerical-continuation-based approaches for computing two phase-response tools, namely, isochrons and phase transition curves. Using examples of the 4d Hodgkin-Huxley model and a 7d sino-atrial node cell, I will show how these approaches are undeterred by sensitivity that is common in biological systems, and how the (n-1)-dimensional isochrons can be computed and visualized even in models with dimension n>3."