Interaction-free measurements were realized using a high-finesse Fabry-Pérot cavity as a measurement apparatus. A figure of merit based on the maximum likelihood estimation, which takes into account real experimental conditions, is used to analyze the efficiency of this measurement scheme. The probability of detecting the presence of an object within the cavity without any photons actually ``hitting'' the object was approximately 85%. The probability of asserting the absence of the object was approximately 75%. Assuming that the a priori probability of the object being present was 1/2, the likelihood of knowing whether the object was present or not was 80%. The obtained results and the limitations of our setup are discussed.