The objective of this work is to examine, in a broad context, the statistical characteristics of the concomitants of generalized order statistics from the Sarmanov family of bivariate distributions. Additionally, a number of recent information measures for concomitants of generalized order statistics based on the Sarmanov and Farlie-Gumbel-Morgenstern families are investigated with comparisons. These measures include weighted entropy, weighted extropy, past extropy, residual extropy, cumulative residual extropy, and negative cumulative residual extropy. In addition, based on concomitants of generalized order statistics, the issue of estimating cumulative residual extropy is investigated using the empirical technique. Also, numerical examples are conducted to illustrate our theoretical findings. Finally, a bivariate real-world data set has been examined for illustration purposes, and the performance is commendable.