We present the analysis of simultaneous X-ray (RXTE) and radio (VLA) observations of two atoll-type neutron star X-ray binaries: 4U 1820 - 30 and Ser X-1. Both sources were steadily in the soft (`banana') X-ray state during the observations. We have detected the radio counterpart of 4U 1820 - 30 at 4.86 and 8.46 GHz at a flux density of ~0.1 mJy. This radio source is positionally coincident with the radio pulsar PSR 1820 - 30A. However, the radio emission of the pulsar falls rapidly with frequency (~ν-3), and we argue that the radio emission of the X-ray binary is dominant above ~2 GHz. Supporting this interpretation, comparison with previous observations reveals variability at the higher radio frequencies that is likely to be due to the X-ray binary. We have detected for the first time the radio counterpart of Ser X-1 at 8.46 GHz, also at a flux density of ~0.1 mJy. The position of the radio counterpart has allowed us to identify its optical counterpart unambiguously. We briefly discuss similarities and differences between the disc-jet coupling in neutron star and black hole X-ray binaries. In particular, we draw attention to the fact that, contrary to other states, neutron star X-ray binaries seem to be more radio-loud than persistent black hole candidates when the emission is `quenched' in the soft state.