Summary: In immunoassay, a nonlinear heteroscedastic regression model is used to characterize assay concentration-response, and the model fitted to data from standard samples is used to calibrate unknown test samples. Usual large-sample methods to construct individual confidence intervals for calibrated concentrations have been observed in empirical studies to be seriously inaccurate in terms of achieving the nominal level of coverage. We show theoretically that this inaccuracy is due largely to estimation of parameters characterizing assay response variance. By exploiting the theory, we propose a bootstrap procedure to adjust the usual intervals to achieve a higher degree of accuracy. We provide both theoretical results and simulation evidence to show that the proposed method attains the nominal level. A practical advantage of the procedure is that it may be implemented reliably using far fewer bootstrap samples than are needed in other resampling schemes.