We present fully traceable two-parameter Hückel equations with parameters B and b1 for the activity coefficient of sodium chloride and for the osmotic coefficient of water in aqueous NaCl solutions at temperatures from (353.15 to 383.15) K. In our most successful parametrization of these equations, parameter B is treated as a constant whereas b1 is a quadratic function of the temperature. The new calculations extend the tables presented up to 353.15 K in our previous study (Partanen, J. I.; Partanen, L. J.; Vahteristo, K. P. J. Chem. Eng. Data 2017, 62, 2617-2632), showing that our Hückel equations apply up to 383.15 K. We also present fully traceable activity quantities from (273.15 to 383.15) K for dilute KCl solutions. Our equations apply to these solutions at least up to a molality of 0.2 mol·kg-1. This article contains the most important new test results of the Hückel equations, where the literature data have been obtained by direct and isopiestic vapor measurements and boiling-point determinations at various pressures. In forthcoming studies, the test results obtained using these equations from KCl solutions will be published for the existing calorimetric data. On the basis of the extensive testing of our models against the experimental data available, the new tables contain the most reliable values of activity and osmotic coefficients for dilute NaCl and KCl solutions published so far. Finally, we report vapor pressures of water in NaCl and KCl solutions above 383 K up to 473 K. These values are obtained with a new and simplified parametrization of the Hückel equation, and our tests show that the parametrization applies well up to a molality of 6 mol·kg-1 in both cases at the high temperatures.