We report on low temperature transport measurements on carbon nanotube Josephson junctions. We use a multiwall carbon nanotube (MWNT) as weak link and niobium as superconductor. To prevent premature switching of the junction we employ an on-chip resistive environment which provides damping at the plasma frequency. Depending on the applied gate, we observe both supercurrent and Coulomb blockade. In the superconducting region we find supercurrent up to 30 nA, the IV characteristics are hysteretic and show phase diffusion. We fit the temperature dependence of the switching current with an extended RCSJ model where a temperature independent critical current is used as a fitting parameter. In the Coulomb blockade region we focus on the magnetic field dependence of the linear conductance and find a splitting of the Coulomb peaks.