The high-viscosity residual fractions obtained during the secondary processing of crude oil are widely used as components in the production of marine fuels. Because of the high viscosity of these residual fractions, they cannot be used as marine fuel in accordance with the ISO 8217 standard (which monitors the quality parameters of residual marine fuels) without being mixed with a suitable low-viscosity cutter stock. Hot filtration, in accordance with the standardized procedures ISO 10307-1 and ISO 10307-2, is used to monitor the stability of the final marine fuels. However, this procedure cannot be applied to pure residual fractions because of their viscosity. We propose a procedure that does allow the application of hot filtration to determine the stability (in accordance with ISO 10307-1 and -2) of high-viscosity residual fractions. The proposed procedure involves mixing the residual fractions with a mixture of methyl esters in a suitable ratio. In this case, a 30% by weight addition of methyl esters to the tested high-viscosity residual fractions was determined to be the most suitable. The SV coefficient was employed to determine the optimal amount of the mixture of methyl ester (C ̌SN EN 14214) diluting component used to evaluate the high-viscosity residual fractions. The resulting values of TS (total sediment) and TSA (total sediment accelerated) parameters showed a high correlation, mainly for the most monitored parameter TSA, with dynamic viscosity at a temperature of 150 °C (R 2 TSA = 0.914) and C/H ratio (R 2 TSA = 0.929). Dependence of DV 150 and C/H ratio on asphaltene content representing n-heptane soluble material in residual fractions, as well as precursors of residual fraction instability, was also monitored. Determining the stability of pure residual fractions helps prevent possible technological problems arising during the storage and transport of either pure residual fractions or prepared marine fuels.