LOFAR will detect all pulsars within 2 kiloparcs (about 6500 light-years) from the sun and discover about 1000 new nearby pulsars at high latitudes. Most of these are expected to emit strongly linearly polarised signals at low frequencies. This allows us to measure their Faraday rotation measures which will give a unprecedented picture of the structure of the magnetic field near to the sun. The strong polarisation also makes them ideal calibration sources for polarisation observations of much weaker sources.