In some Resistive Random Access Memories, the high and low resistance states (HRS and LRS, respectively) are associated to the creation (Set) and disruption (Reset) of a conductive filament (CF) that locally connects or disconnects the electrodes. Usually, a current limit (CL) must be fixed during the Set process. Typically, these devices are characterized using semiconductor parameter analyzers (SPA), which have a low sampling rate and a somehow uncontrolled current limitation mechanism. In this work, a lowcost setup with large sampling rate and a well-controlled widerange current limiting unit is presented. The system is suitable to capture fast transients during the Set/Reset processes and to detect Random Telegraph Noise unresolvable by SPAs. These measurements can be combined with a Conductive Atomic Force Microscope, to get information on CF properties that cannot be directly measured with SPAs, as the spatial distribution of current in the CF at LRS and HRS.