Devices with metallic nanoconstrictions functionalized by organic molecules are promising candidates for the role of functional devices in molecular electronics. However, at the moment little is known about transport and noise properties of nanoconstriction devices of this kind. In this paper, transport properties of bare gold and molecule-containing tunable cross-section nanoconstrictions are studied using low-frequency noise spectroscopy. Normalized noise power spectral density (PSD) S I /I 2 dependencies are analyzed for a wide range of sample resistances R from 10 Ohm to 10 MOhm. The peculiarities and physical background of the flicker noise behavior in the low-bias regime are studied. It is shown that modification of the sample surface with benzene-1,4-dithiol molecules results in a decrease of the normalized flicker noise spectral density level in the ballistic regime of sample conductance. The characteristic power dependence of normalized noise PSD as a function of system resistance is revealed. Models describing noise behavior for bare gold and BDT modified samples are developed and compared with the experimental data for three transport regimes: diffusive, ballistic and tunneling. Parameters extracted from models by fitting are used for the characterization of nanoconstriction devices.