A method is developed for calculating asymptotic confidence intervals for estimates of abundance obtained from trawl surveys conducted by means of the swept area method, using likelihood ratios from Aitchison's delta distribution. Simulation tests of the method show that unbiased estimates of density and biomass can be obtained and that the estimated confidence intervals have close to the nominal coverage probability. Performance deteriorates in cases where few of the hauls contain fish and the coefficient of variation (CV) is high. The upper confidence bound appears to be slightly less reliable than the lower.