In the study of nonlinear dynamical systems, it is useful to determine the (parameter space) phase boundary that separates stable from unstable behaviour. This presentation will consider algorithms which achieve that goal through the use of shooting methods and Euler homotopy continuation. Firstly, the trajectory is forced to remain in the proximity of an unstable equilibrium point (UEP) for a specified time. That time is then progressively increased, ensuring the trajectory approaches the UEP arbitrarily closely. This process can be used to explore trade-offs between parameters. It also forms the basis for robustness assessment by establishing the minimum distance (in parameter space) from a given operating point to the phase boundary. The various concepts will be illustrated through examples that consider "fault induced delayed voltage recovery" (FIDVR), a vulnerability of distribution networks where residential air-conditioning is prevalent.