The Chebyshev polynomial fitting (CPF) method has been proved to be effective to construct reliable cotidal charts for the eight major tidal constituents (M2, S2, K1, O1, N2, K2, P1, and Q1) and six minor tidal constituents (2N2, J1, L2, Mu2, Nu2, and T2) near Hawaii in Part I and Part II, respectively. In this paper, this method is extended to estimate the harmonic constants of four long-period tidal constituents (Mf, Mm, Sa, and Ssa). The harmonic constants obtained by this method were compared with those from the TPXO9, Finite Element Solutions 2014 (FES2014), and Empirical Ocean Tide 20 (EOT20) models, using benchmark data from satellite altimeters and eight tide gauges. The accuracies of the Mf and Mm constituents derived from the CPF method are comparable to those from the models, but the accuracies of the Sa and Ssa constituents are significantly higher than those from the FES2014 and EOT20 models. The results indicate that the CPF method is also effective for estimating harmonic constants of long-period tidal constituents. Furthermore, since the CPF method relies only on satellite altimeter data, it is an easier-to-use method than these ocean tide models.