Recently, Wu in 2018 established interesting results in the framework of interval spaces. He initiated the idea of near-fixed points and proved some related basic results in metric interval, norm interval, and hyperspaces. In 2015, Khojasteh et al. gave the concept of simulation functions and studied some fixed-point results in metric spaces. Motivated by this work, we give some near-coincidence point results in norm interval spaces using the concept given by Khojasteh et al. Examples are also provided for the validation of the results.