Determining the limiting current of an electrolyte is essential when understanding its performance and viable applications. With rechargeable batteries becoming widespread across various industries, it is essential to develop electrolytes that can be utilized in high current applications. These large applied currents are challenging as concentration gradients develop inside the electrolyte, and at high enough currents these gradients can be unsustainable and the limiting current is reached. In single ion conducting materials where the transference number approaches unity, concentration gradients do not form within the electrolyte leading to the potential of sizeable values of limiting current in these materials. Within this work, we discuss measurements of the limiting current for a single ion conducting polymeric electrolyte and compare it to similar measurements for a conventional block copolymer electrolyte. We use a method of comparing the electric potential response to various applied currents to determine the limiting current of these electrolytes. Moreover, we have determined that the limiting current of the single ion conducting electrolyte appears to be independent of electrolyte thickness, which deviates from the linear relationship found in the conventional block copolymer electrolyte.