The Electric Network Frequency (ENF) is a signature of power distribution networks that can be captured by multimedia recordings made in areas where there is electrical activity. This has led to an emergence of several forensic applications based on the use of the ENF signature. Examples of such applications include estimating or verifying the time-of-recording of a media signal and inferring the power grid associated with the location in which the media signal was recorded. In this paper, we carry out a feasibility study to examine the possibility of using embedded ENF traces to pinpoint the location-of-recording of a signal within a power grid. In this study, we demonstrate that it is possible to pinpoint the location-of-recording to a certain geographical resolution using power signal recordings containing strong ENF traces. To this purpose, a high-passed version of an ENF signal is extracted and it is demonstrated that the correlation between two such signals, extracted from recordings made in different geographical locations within the same grid, decreases as the distance between the recording locations increases. We harness this property of correlation in the ENF signals to propose trilateration based localization methods, which pinpoint the unknown location of a recording while using some known recording locations as anchor locations. We also discuss the challenges that need to be overcome in order to extend this work to using ENF traces in noisier audio/video recordings for such fine localization purposes.