The article considers the examples of calculation of catastrophic floods characteristics at ungauged rivers of the Black sea coast of Russia. Mathematical modeling of hydrological processes is proposed as an alternative to the standard methods of assessment of engineering characteristics based on a probabilistic approach in the climate change conditions. The deterministic hydrological model Hydrograph was applied to estimate the maximum water discharges of the ungauged Tsemes river (Novorossiysk). The set of model parameters was developed and verified at studied catchments. Continuous simulations of streamflow were conducted at the Tsemes River with a daily resolution for the period 1977-2013. Using detailed pluviograms data of storm precipitation at Novorossiysk and nearby meteorological stations, 1-hour maximum water discharge of three catastrophic floods on Tsemes river was calculated for flood events in 1988, 2002 and 2012 and compared with the characteristics of maximum discharges obtained on the basis of calculations according to the standard methods SP-33-101-2003 (SP). The maximum simulated discharges in 2002 and 2012 were 284 and 361 m3/s and correspond to maximum discharges of 1% probability calculated on the basis of the SP. However, estimated water discharge for the catastrophic flood in 1988 reached 688 m3/s, which is twice the value of 1% probability estimated with standard methods. The analysis of the simulation results has shown that the maximum discharge depends on the antecedent state of the catchment, which cannot be explicitly taken into account when using probabilistic calculation methods. The possibility of using mathematical modeling as an approach for assessment of probable maximum flood (PMF), which allows taking into account the combination of the most unfavorable meteorological and runoff formation factors that can lead to the occurrence of PMF, is discussed. The development of methods based on the integrated use of mesoscale atmospheric models and deterministic hydrological models is important as a prospect. The developed methods for assessing the frequency and magnitude characteristics of catastrophic floods can be used to solve engineering problems in climate change conditions.