An exemplary system may include a sound processor that is communicatively coupled to a cochlear implant implanted within a patient. The cochlear implant may include a current generation circuit (402) in series with a capacitor (418) and a voltage measurement circuit (422). The sound processor may 1) direct the cochlear implant to enable the current generation circuit for a time interval, causing a current to flow to the capacitor, 2) direct the cochlear implant to use the voltage measurement circuit to measure a voltage change across the capacitor that occurs during the time interval, and 3) determine a current level of the current that flows from the current generation circuit to the capacitor. A corresponding method is also described.