The concordance correlation coefficient (CCC) is a common measure of reproducibility or agreement between data values in paired samples. Confidence intervals and hypothesis tests of the CCC using normal approximations (NA) have been shown to have poor coverage for highly skewed distributions. This study applies the jackknife empirical likelihood (JEL) to confidence intervals for the CCC and compares coverage probability and interval length for JEL and NA methods. Data are simulated for CCC values between 0.25 - 0.95 from normal and non-normal distributions of varying skewness. Simulation results showed that JEL methods perform better than the NA methods particularly with data from skewed distributions.The JEL methods have the widest confidence intervals in most cases. Application of JEL methods are illustrated by evaluating concordance between self-reported and clinically measured body weight and height from the National Health and Nutrition Examination Survey (NHANES).