The accuracy of two empirical formulae used in recent climatological studies to estimate the atmospheric longwave flux at the ocean surface from ship meteorological reports has been evaluated using research cruise measurements from the northeast Atlantic. The measurements were obtained with a pyrgeometer and corrected for differential heating of the pyrgeometer dome and shortwave transmission through the dome. The formulae tested were from Clark et al. <1974> and Bignami et al. <1995>; neither was capable of providing consistently reliable estimates of the longwave flux. Clark overestimated the mean measured longwave of 341.1 Wm-2 by 11.7 Wm-2, while Bignami underestimated by 12.1 Wm-2. A new formula is developed that expresses the effects of cloud cover and other parameters on the longwave through an adjustment to the measured air temperature. The air temperature is adjusted by the amount necessary to obtain the effective temperature of a blackbody with a radiative flux equivalent to that from the atmosphere. A simple parameterization of the adjustment in terms of the total cloud amount gives longwave estimates that have an improved mean bias error with respect to the measurements of -1.3 Wm-2. The new formula is still biased under overcast, low cloud base conditions. However, by including a dependence on dew point depression in the formula, this bias is resolved, and the mean error reduced to 0.2 Wm-2. The new formula has been tested using measurements made on two subsequent cruises and found to agree to within 2 Wm-2 in the mean at middle-high latitudes.