The margin, or the difference between the received signal-to-noise ratio (SNR) and the SNR required to maintain a given bit error ratio (BER), is important to the design and operation of optical amplifier transmission systems. A new technique is described for estimating the SNR at the receiver's decision circuit when the BER is too low to be measured in a reasonable time. The SNR is determined from the behavior of the BER as a function of the decision threshold setting in the region where the BER is measurable. We obtain good agreement between the BER predicted using the measured SNR value and the actual measured BER.