Two methods have been developed to measure variations with magnetic field of electrical resistances in the range 0.1 n&OHgr;–1 &mgr;&OHgr;, for applied magnetic fields up to 3 T, and for temperatures less than 9 K. The first method provides direct access toR(H). Its absolute sensitivity is 3×10−14V/&sqrt;Hz with a short circuit at input. It becomes on a 1 &mgr;&OHgr; sample: 6×10−14V/&sqrt;Hz in zero field, and 2×10−12V/&sqrt;Hz under 3 T. Averaging the signal over 100 s, the sensitivity is 6×10−15V in zero field and 2×10−13V under 3 T. In terms of resistance, using a sensing current of 100 mA, it corresponds to a sensitivity of 6×10−14&OHgr; in zero field and 2×10−12&OHgr; in the maximum field. The reproducibility of this method is 0.3%. The second method is a sinusoidal field modulation technique giving the field derivative of the resistance:dR/dH. It has the same absolute sensitivity as theR(H) method and it achieves ultrahigh resolution. It is sensitive to variations of the resistance as small as 6×10−14&OHgr; in zero field and 2×10−12&OHgr; in 3 T independent of the absolute resistance of the sample, thus the resulting resolution &Dgr;R/Ris, for example, 6×10−8in zero field and 2×10−6in the maximum field for a 1 &mgr;&OHgr; sample. To demonstrate the high sensitivity of the setups, we measured the magnetoresistance of a magnetic multilayer with the current applied perpendicular to the multilayer plane. ©1996 American Institute of Physics.