The motion of Charge-Density Waves (CDWs) shows many similarities with transport in superconductors with the role of voltage and current reversed. Submicron superconducting devices are very important in both fundamental studies and applications of superconductivity. For CDWs, reliable fabrication methods for making similar devices are not as advanced and are still being developed. In search for new mesoscopic CDW physics, we have fabricated insulating longitudinal point contacts and weak links in the CDW conductor NbSe 3. We have found conductance peaks at energies corresponding to the Peierls gap when the temperature is brought below the transitions. The peaks follow a mean-field theory temperature dependence, indicating that the transport through these devices are spectroscopy measurements. The insulating point contacts show tunnelling behaviour similar to SIS junctions, while the weak links show transport similar to SNS junctions. These devices allow us to study the CDW analogies of superconductors such as the Josephson relations, Andeev reflection, subgap features of phonon modes due to electron-phonon coupling and pair-breaking at high velocities.