This paper presents the design of passives for an ultracapacitor (UC) based dc-dc power supply which provides energy backup to critical loads in case of momentary power main failures. Unlike in a typical bidirectional dc-dc converter, in a UC based bidirectional converter, the interfacing inductor design has to accommodate both charging and discharging operations for wide variations in UC stack voltage, Vuc. This paper not only provides such a design but also analyzes the inductance variation for wide range of design applications. In the process, a mathematical relation between operating power, Po and switching frequency, fsw for a generalized power electronic converter is proposed. Further the design of UC stack is also provided using which the variation of capacitance of the stack, Cuc and Equivalent Series Resistance (ESR), Ruc of the stack is analyzed for wide range of design applications. Such a generalized design of passives for a UC based backup system is crucial for reasons such as to carry out performance studies on the backup system or for validating an ultracapacitor model for a wide range of operating power and voltage levels suiting various design applications. Based on the design presented in this paper, the UC stack and inductor are realized physically whose functionality is verified experimentally using a 250W experimental set-up operated at a power level of 120W.