A detailed spectroscopic study of 11 giants with spectral type from G9 to M2 is presented. The 2.38-4.08 mum wavelength-range of band 1 of ISO-SWS (Short-Wavelength Spectrometers on board of the Infrared Space Observatory) in which many different molecules - with their own dependence on each of the stellar parameters - are absorbing, enables us to estimate the effective temperature, the gravity, the microturbulence, the metallicity, the CNO-abundances, the C-12/C-13-ratio and the angular diameter from the ISO-SWS data. Using the Hipparcos' parallax, the radius, luminosity and gravity-inferred mass are derived. The stellar parameters obtained are in good agreement with other published values, though also some discrepancies with values deduced by other authors are noted. For a few stars (delta Dra, xi Dra, alpha Tuc, H Sco and alpha Cet) some parameters - e.g. the CNO-abundances - are derived for the first time. By examining the correspondence between different ISO-SWS observations of the same object and between the ISO-SWS data and the corresponding synthetic spectrum, it is shown that the relative accuracy of ISO-SWS in band 1 (2.38-4.08 mum) is better than 2% for these high-flux sources. The high level of correspondence between observations and theoretical predictions, together with a confrontation of the estimated T-eff (ISO) value with T-eff values derived from colours - which demonstrates the consistency between V - K, BCK, T-eff and theta(d) derived from optical or IR data - proves that both the used MARCS models to derive the stellar quantities and the flux calibration of the ISO-SWS detectors have reached a high level of reliability.