Summary: The main objective of this article is to obtain some new estimates related to Hermite-Hadamard-like integral inequalities essentially using the class of \(h\)-convex functions. For this we first derive a new integral identity which will serve as an auxiliary result for obtaining the main results of the article. Several new and known special cases are also discussed. In the last some applications to means of real numbers are also discussed in detail which elaborates the significance of the obtained results.