In the present study, we used three strains of mice with various susceptibility to stress: mice with knock-out of the gene encoding norepinephrine transporter (NET-KO), which are well characterized as displaying a stress-resistant phenotype, as well as two strains of mice displaying two different stress-coping strategies, i.e., C57BL/6J (WT in the present study) and SWR/J. The procedure of restraint stress (RS, 4 h) was applied, and the following behavioral experiments (the forced swim test and sucrose preference test) indicated that NET-KO and SWR/J mice were less sensitive to RS than WT mice. Then, we aimed to find the miRNAs which changed in similar ways in the serum of NET-KO and SWR/J mice subjected to RS, being at the same time different from the miRNAs found in the serum of WT mice. Using Custom TaqMan Array MicroRNA Cards, with primers for majority of miRNAs expressed in the serum (based on a preliminary experiment using the TaqMan Array Rodent MicroRNA A + B Cards Set v3.0, Thermo Fisher Scientific, Waltham, MA, USA) allowed the identification of 21 such miRNAs. Our further analysis focused on miR-1 and miR-155 and their targets—these two miRNAs are involved in the regulation of BDNF expression and can be regarded as biomarkers of stress-resilience.