A self-terminated electrochemical method was used to fabricate microscopic-scale contacts between two Au electrodes in a microfluidic channel. The conductance of contacts varies in a stepwise fashion showing quantization near the integer multiples of the conductance quantum ( ). The mechanism works by a pressure-driven flow parallel to a pair of Au electrodes with a gap on the order of micron in an electrolyte of HCl. When applying a bias voltage between two electrodes, metal atoms are etched off the anode and dissolved into the electrolyte as metal ions, which are then deposited onto the cathode. Consequently, the gap decreases to the atomic scale and then completely closes as the two electrodes form a contact. The electrochemical fabrication approach introduces large variance in the formation and location of individual junctions. Understanding and controlling this process will enable the precise positioning of reproducible geometries into nano-electronic devices.