Microfluidic-drop networks consist of several stable drops—interconnected through microfluidic channels—in which organ models can be cultured long-term. Drop networks feature a versatile configuration and an air–liquid interface (ALI). This ALI provides ample oxygenation, rapid liquid turnover, passive degassing, and liquid-phase stability through capillary pressure. Mathematical modeling, e.g., by using computational fluid dynamics (CFD), is a powerful tool to design drop-based microfluidic devices and to optimize their operation. Although CFD is the most rigorous technique to model flow, it falls short in terms of computational efficiency. Alternatively, the hydraulic–electric analogy is an efficient “first-pass” method to explore the design and operation parameter space of microfluidic-drop networks. However, there are no direct electric analogs to a drop, due to the nonlinear nature of the capillary pressure of the ALI. Here, we present a circuit-based model of hanging- and standing-drop compartments. We show a phase diagram describing the nonlinearity of the capillary pressure of a hanging drop. This diagram explains how to experimentally ensure drop stability. We present a methodology to find flow rates and pressures within drop networks. Finally, we review several applications, where the method, outlined in this paper, was instrumental in optimizing design and operation.