Aims: We determine the effective temperature, surface gravity and projected rotational velocity of nine T dwarfs from the comparison of high-resolution near-infrared spectra and synthetic models, and estimate the mass and age of the objects from state-of-the-art models. Methods: We use the AMES-COND cloudless solar metallicity models provided by the PHOENIX code to match the spectra of nine T-type field dwarfs observed with the near-infrared high-resolution spectrograph NIRSPEC using ten echelle orders to cover part of the J band from 1.147 to 1.347 μm with a resolving power R˜20 000. The projected rotational velocity, effective temperature and surface gravity of the objects are determined based on the minimum root mean square of the differences between the modelled and observed relative fluxes. Estimates of the mass and age of the objects are obtained from effective temperature-surface gravity diagrams, where our results are compared with existing solar metallicity models. Results: The modelled spectra reproduce quite well the observed features for most of the T dwarfs, with effective temperatures in the range of 922-1009 K, and surface gravities between 104.1 and 104.9 cm s-2. Our results support the assumption of a dust free atmosphere for T dwarfs later than T5, where dust grains form and then gravitationally sediment into the low atmosphere. The modelled spectra do not accurately mimic some individual very strong lines like the K i doublet at 1.2436 and 1.2525 μm. Our modelled spectra does not match well the observed spectra of the two T dwarfs with earlier spectral types, namely SDSSp J125453.90-012247.4 (T2) and 2MASS J05591914-1404488 (T4.5), which is likely due to the presence of condensate clouds that are not incorporated in the models used here. By comparing our results and their uncertainties to evolutionary models, we estimate masses in the interval ≈5-75~MJ for T dwarfs later than T5, which are in good agreement with those found in the literature. We found apparent young ages that are typically between 0.1 and a few Gyr for the same T dwarfs, which is consistent with recent kinematical studies. Reduced NIRSPEC spectra of the nine T-type dwarfs are available electronically in fits format at the CDS via anonymous ftp to cdsarc.u-strasbg.fr (130.79.128.5) or via http://cdsweb.u-strasbg.fr/cgi-bin/qcat?J/A+A/501/1059