This paper develops a new approach to the assessment of the boundedness/stability of some vector nonlinear systems with delays and variable coefficients. The approach rests on the development of scalar counterparts to the original vector systems. We show that the solutions to these scalar auxiliary nonlinear equations with delay and variable coefficients bound from the above the norms of solutions to the original equations with the matched history functions. This prompts the assessment of the boundedness/stability traits of the vector systems through the abridged evaluation of the dynamics of their scalar counterparts. The latter task is achieved in effortless simulations or through the application of simplified analytical inferences. Consequently, we convey some novel boundedness/ stability criteria and estimate the radiuses of the balls imbedded in the boundedness/stability regions. Lastly, we authenticate our inferences in representative simulations that also measure their accuracy. This prompts the evaluation of the boundedness/stability properties of nonautonomous VNDS through the assessment of dynamics of their scalar counterparts that can be triggered in effortless simulations or abridged analytical reasoning. Consequently, we derive some novel boundedness/stability criteria and estimate the radiuses of the balls that are immersed in the boundedness/stability regions of the original systems. Lastly, we authenticate the developed approach in representative simulations that also measure the accuracy of these techniques. This paper is organized as follows. The next section outlines our notation, some preliminary statements, and defines the underlined system. Section 3 ascribes the reduction technique and its applications to the evaluation of the boundedness/stability of some VNDS with variable coefficients. Section 4 presents a closed-form stability criterion. Section 5 discusses the applications of linearized auxiliary equations. Section 6 highlights the results of our simulations, and Section 7 concludes this study and outlines some directions for subsequent research.