Since the discovery of companions to B1257+12, it has been known that planets can exist around pulsars. Such planets may be formed in discs analogous to those around young stars, so we have searched for dust grain emission towards a sample of nine nearby millisecond pulsars, No emission is detected down to typical 2 sigma limits of 5 mJy, at a wavelength of 850 mu m, Using a model in which grains are heated by the pulsar spin-down luminosity, these dust flux limits correspond to disc masses of typically less than or equal to 10 Earth masses. The low dust limits show that nearby pulsar planets must already exist, rather than be in the process of forming, but only B1257+12 is known to have such planets. Planetary systems appear to occur around only a few per cent of pulsars and main-sequence stars, and are thus a rare phenomenon irrespective of circumstellar environment.