New developments in studies of ultra-thin nanowires indicate on a possibility to transfer electrons through a narrow metal nanobridge at room temperature without energy loss. The underlying phenomenon, not due to superconductivity, is associated with ballistic electron transfer in short and very narrow nanobridges. In this work, the quantum confinement effects in metallic conductance phenomena in metal nanobridges were investigated. The nanobridge devices with small atomic-wide gap were formed by a novel controlled electroplating method on a nanolithographed quartz wafer. The field-induced formation of monatomic Ni and Cu nanobridges are described. In the absence of an electric field, the Ni nanowires are unstable and disassemble quickly due to high surface mobility of metal adatoms. Exceptionally stable monatomic quantum nanobridges were obtained by chemical treatment. They were investigated in the dry state and in electrolyte solutions. The quantum conductance with zero temperature coefficient was observed at low electric field strength (bias voltage |Vb| < 0.3 V). Deviations observed at higher field strengths have been attributed to thermally activated electron transfer through the nanobridge.