We report the production of vertically aligned and interconnected ZnO core/shell nanorods using pulsed laser deposition (PLD) in a continuous two-step growth process. X-ray diffraction studies showed wurtzite structure and c-axis orientation with a high degree of verticality. Scanning electron microscopy showed a characteristic interconnection morphology between the nanorod tips uniformly present over the entire sample surface area, while transmission electron microscopy revealed crystalline core/amorphous shell architecture. Strong bands at 98.7 cm-1 and 437.2 cm-1 (wurtzite ZnO low and high nonpolar E2 modes) were the main features of the nanorod Raman spectra, again showing the high sample quality. Low-temperature PL data exhibited strong I6 emission and structured green band showing high optical quality. Electrical studies indicated n-type material with ohmic behaviour. The results are discussed in the context of the advantages offered by interconnected architectures of core/shell ZnO nanostructures for various applications.