It is always difficult to monitor stringent cell loss ratio (CLR), e.g. 10-9, in asynchronous transfer mode (ATM) networks, because its measurement period is too long for real-time measurement. In this paper, we propose new performance monitoring mechanisms for stringent CLR. We consider virtual ATM switches whose resources are much smaller than the real system and thus much higher CLRs will be obtained within a relatively short measurement period. By applying some regression methods in the CLRs obtained from the virtual system, we can estimate the actual CLR of the real system quite accurately and our performance monitoring mechanisms will be operated based on the estimation. Through the numerical examples, our mechanisms are not only more accurate than the traditional methods, but also have shorter measurement periods compared with direct measurement.