An integrated electronic system is provided with a package formed by a support base and a coating region arranged on the support base and having at least a first system die, including semiconductor material, coupled to the support base and arranged in the coating region. The integrated electronic system also has, within the package, a monitoring system configured to determine the onset of defects within the coating region, through the emission of acoustic detection waves and the acquisition of corresponding received acoustic waves, whose characteristics are affected by, and therefore are indicative of, the aforementioned defects.