[en] We present a high-precision infrared radial velocity (RV) study of late-type stars using spectra obtained with NIRSPEC at the W. M. Keck Observatory. RV precisions of 50 m s^–1 are achieved for old field mid-M dwarfs using telluric features for wavelength calibration. Using this technique, 20 young stars in the β Pic (age ∼ 12 Myr) and TW Hya (age ∼ 8 Myr) Associations were monitored over several years to search for low-mass companions; we also included the chromospherically active field star GJ 873 (EV Lac) in this survey. Based on comparisons with previous optical observations of these young active stars, RV measurements at infrared wavelengths mitigate the RV noise caused by star spots by a factor of ∼3. Nevertheless, star spot noise is still the dominant source of measurement error for young stars at 2.3 μm, and limits the precision to ∼77 m s^–1 for the slowest rotating stars (v sin i < 6 km s^–1), increasing to ∼168 m s^–1 for rapidly rotating stars (v sin i > 12 km s^–1). The observations reveal both GJ 3305 and TWA 23 to be single-lined spectroscopic binaries; in the case of GJ 3305, the motion is likely caused by its 0.''09 companion, identified after this survey began. The large amplitude, short-timescale variations of TWA 13A are indicative of a hot Jupiter-like companion, but the available data are insufficient to confirm this. We label it as a candidate RV variable. For the remainder of the sample, these observations exclude the presence of any 'hot' (P < 3 days) companions more massive than 8 M_Jup and any 'warm' (P < 30 days) companions more massive than 17 M_Jup, on average. Assuming an edge-on orbit for the edge-on disk system AU Mic, these observations exclude the presence of any hot Jupiters more massive than 1.8 M_Jup or warm Jupiters more massive than 3.9 M_Jup.