Experimental data with unprecedented submicrometre resolution obtained in a phase-contrast radiography experiment in a magnifying configuration are presented. The term 'phase contrast' here indicates that the phase retardation of coherent light in matter was utilized as the contrast mechanism. The coherent and divergent beam exiting an X-ray waveguide was used in a lensless configuration to magnify spatial variations in optical path length up to several hundred times. The defocused image of a nylon fibre was measured with a resolution of 0.14 micro m at the object. Sufficient contrast was found for exposure times of 0.1 s, i.e. in the regime for real-time studies.