We present new Hubble Space Telescope (HST)/Cosmic Origins Spectrograph (COS) observations of the narrowline Seyfert 1 galaxy NGC 4051. These data were obtained as part of a coordinated observing program including X-ray observations with the Chandra/High Energy Transmission Grating (HETG) spectrometer and Suzaku. We detected nine kinematic components of UV absorption, which were previously identified using the HST/Space Telescope Imaging Spectrograph (STIS). None of the absorption components showed evidence for changes in column density or profile within the ∼10 yr between the STIS and COS observations, which we interpret as evidence of (1) saturation, for the stronger components, or (2) very low densities, i.e., n H < 1 cm −3 , for the weaker components. After applying a + 200 km s −1 offset to the HETG spectrum, we found that the radial velocities of the UV absorbers lay within the O vii profile. Based on photoionization models, we suggest that, while UV components 2, 5, and 7 produce significant O vii absorption, the bulk of the X-ray absorption detected in the HETG analysis occurs in more highly ionized gas. Moreover, the mass-loss rate is dominated by high-ionization gas which lacks a significant UV footprint.