In the framework of mechanisms for color confinement as well as in  various statistical models, disorder parameters can be developed which are  generally expressed as ratios of partition functions and whose numerical determination can be challenging. We develop an efficient method for their  computation and apply it to the study of dual superconductivity in 4$d$  compact $U(1)$ gauge theory. The method can be applied in a straightforward  way to a wide class of similar problems.