The development of robust software is a difficult undertaking and is becoming increasingly more important as applications grow larger and more complex. Although modern programming languages such as C++ and Java provide sophisticated exception handling mechanisms to detect and correct runtime error conditions, exception handling code must still be programmed with care to preserve application consistency. In particular, exception handling is only effective if the premature termination of a method due to an exception does not leave an object in an inconsistent state. We address this issue by introducing the notion of failure atomicity in the context of exceptions. We propose practical techniques to automatically detect and mask the nonatomic exception handling situations encountered during program execution. These techniques can be applied to applications written in various programming languages that support exceptions. We perform experimental evaluation on both C++ and Java applications to demonstrate the effectiveness of our techniques and measure the overhead that they introduce.