Excitation functions were measured for the $^{55}$Mn(n,2n)$^{54}$Mn, $^{55}$Mn(n,$alpha$)$^{52}$V, $^{63}$Cu(n,$alpha$)$^{60}$Co, $^{65}$Cu(n,2n)$^{64}$Cu, and $^{65}$Cu(n,p)$^{65}$Ni reactions from 13.47 to 14.83 MeV. The experimental cross sections are compared with the results of calculations including all activation channels for the stable isotopes of Mn and Cu, for neutron incident energies up to 50 MeV. Within the energy range up to 20 MeV the model calculations are most sensitive to the parameters related to nuclei in the early stages of the reaction, while the model assumptions are better established by analysis of the data in the energy range 20-40 MeV. While the present analysis has taken advantage of both a new set of accurate measured cross sections around 14 MeV and the larger data basis fortunately available between 20 and 40 MeV for the Mn and Cu isotopes, the need of additional measurements below as well as above 40 MeV is pointed out. Keywords: 55Mn, 63,65Cu, E$leq$40 MeV, Neutron activation cross section measurements, Nuclear reactions, Model calculations, Manganese, Copper