The Very Large Array (VLA) in Socorro, New Mexico, has been used to measure the 6 cm continuum flux densities and the angular sizes of 42 planetary nebulae (PN) in the direction of the galactic centre (GC). These were all optically confirmed PN for which the radial velocities (and positions on the sky) make it very likely that they are close to the GC. With a detection limit of about 1 mJy, 34 PN were detected. Their flux densities range from 2 to 100 mJy. Initially we used a configuration of the VLA with an instrumental resolution of 1″. About 80% of the detected PN could be clearly resolved with this resolution. The unresolved PN were observed again with a configuration of the VLA that has a resolution of 0″.4. For all but one of the 34 detected PN we could determine reliable angular sizes. The inferred total ionized masses range from < 0.01 to ~ 0.5 M⊙, assuming a distance to the GC of 9 kpc. The results argue strongly against the use of the Shklovsky method for distance determinations. Previous measurements of PN at the GC showed that their luminosities were substantially higher than those for nearby PN (Pottasch, 1980). The luminosity distribution of the PN in our sample is broader towards lower luminosities (up to the detection limit of the observations), but the luminosities are still high compared with nearby PN. We interpret this as a selection effect: by studying only optically confirmed PN, the intrinsically brightest PN are selected.