A new technique for detecting and measuring magnetic fields on cool stars is presented, incorporating both an improved observational approach and a rigorous LTE theoretical treatment. We have identified two lines in the near infrared, one of which is very sensitive to Zeeman broadening and the other relatively insensitive, that are easily accessible to CCD and Reticon detectors. The lines are modelled by solving numerically the equations of transfer for the Stokes parameters in a full model atmosphere, permitting computation of all relevant depth-dependent physics such as polarized line opacities and broadening sources. We have obtained high resolution, high S/N spectroscopic observations of several G and K dwarfs and have synthesized the two lines using two free parameters, namely, the average field strength, B, and the fraction, f, of the surface covered by fields. For the chromospherically active stars ε Eridani and Xi Boo A, we find B=1000, f=35% and B=1200, f=40%, respectively. A careful study has been made of various sources of broadening to determine their ability to mimic Zeeman broadening, and none is capable of doing so.