Current measurements in a wide dynamic range from low picoamperes up to a few milliamperes are usually carried by implementing logarithmic current-to-voltage converter circuits. Conductance studies in nanoscale metal | molecule | metal junctions require measurements with a high dynamic range, good accuracy and reasonable speed simultaneously. In this work we propose two novel circuit solutions which comply with these conditions: one is based on a high-accuracy, fine-tunable logarithmic current-to-voltage converter. Another circuit implements a double-output (or multiple-output) linear current-to-voltage converter, for which the problem of range-switching has been circumvented. Both circuits were applied in constructing a low-current bipotentiostat dedicated to the electrochemical formation of molecular-scale gaps, and a novel scanning tunnelling microscope preamplifier stage for current-distance spectroscopy studies.