We have developed a general numerical/analytical theory of non-faradaic impedance of an evaporating droplet, and validated the model by experiments involving droplets of various analyte concentrations deposited on a surface defined by coplanar electrodes. The impedance of the droplet Z(n0,t,f) is analyzed as a function of the concentration (n0) of the ions in the solution, the measurement frequency (f) and the evaporation time (t). We illustrate the versatility of the model by determining the sensitivity enhancement α(t) of the droplet-based impedimetric nano-biosensor under different regimes of operation. The model should have broad applications in the characterization/optimization of droplet-based systems, especially lab-on-chip components involving digital microfluidics.