In deterministic dynamics, a stable limit cycle is a closed, isolated periodic orbit that attracts nearby trajectories. Points in its basin of attraction may be disambiguated by their asympototic phase. In stochastic systems with approximately periodic trajectories, asymptotic phase is no longer well defined, because all initial densities converge to the same stationary measure. We explore circumstances under which one may nevertheless define an analog of the "asymptotic phase". In particular, we consider jump Markov process models incorporating ion channel noise, and study a stochastic version of the classical Morris-Lecar system in this framework. We show that the stochastic asymptotic phase can be defined even for some systems in which no underlying deterministic limit cycle exists, such as an attracting heteroclinic cycle perturbed by additive noise. We also discuss an analysis of an efficient numerical approximation for simulating trajectories of randomly gated ion channels, called the stochastic shielding approximation, recently introduced by Schmandt and Galan (Physical Review Letters, 2012).