The jackknife estimation procedure is used to estimate Brillouin's and Simpson's indices of diversity when sampling is done by selecting quadrats. Using simulated data, a sampling plan is set up to study effects of quadrat size, sample size, and sampling area. The estimates are evaluated by estimating bias, standard error, and mean square error, and by comparing expected 95% confidence interval coverage with observed 95% confidence interval coverage. Smaller quadrats tend to give less biased and smaller variance estimates of Brillouin's index. The jackknife estimate of Simpson's index is unbiased using quadrat samples, but the estimates of standard error appears to be an overestimate for large samples, causing overcoverage (>95%) for observed confidence intervals.