Recently, the Al-Ti alloy with the 70 wt% Al was found to give the most reproducible contact resistivity rho(c) on epitaxial and implanted p-type SiC after vacuum annealing at 1000degreesC for 2 min. In this work contact resistivity values of this Al-Ti alloy are analyzed aiming at extracting the Schottky barrier height with particular attention to p-type ion implanted 4H- and 6H-SiC specimens. The rho(c) values extracted from Transmission Line Method measurements were always lower than 2x10(-4) Omegacm(2) for a medium/high doping concentration of the implanted layers, i.e. 4x10 cm(-3) Moreover, a significant portion of values below the minimum resolution of 1x10(-6) Omegacm(2) was found. The barrier height phi(B) has been extracted from the contact resistivity as a function of the temperature, according to the thermionic-field emission model, for all the dies featuring a rho(c) greater than the minimum resolution. For these dies the phi(B) is (0.53+/-0.05) eV for the 6H-SiC epilayer, (0.82+/-0.08) eV for the implanted 4H-SiC and (0.95+/-0.08) eV for the implanted 6H-SiC. It was found that the dies which have a rho(c) minor than the minimum resolution could feature a barrier height similar to that found on the epilayer.