We describe the fabrication and measurement of one-dimensional series arrays of small capacitance Josephson junctions and superconducting quantum interference devices. These arrays exhibit a Coulomb blockade of Cooper pair tunneling when the Josephson coupling energy is the order of the charging energy. The effectiveness of a resistive coaxial cable (Thermocoax(TM) made by Philips) for attenuation of high frequency electromagnetic noise is demonstrated. This noise influences the measured de current-voltage characteristic of the array, having qualitatively the same effect as raising the temperature.