ABSTRACT Reverberation-mapping-based scaling relations are often used to estimate the masses of black holes from single-epoch spectra of active galactic nuclei (AGNs). While the radius-luminosity relation that is the basis of these scaling relations is determined using reverberation mapping of the Hβ line in nearby AGNs, the scaling relations are often extended to use other broad emission lines, such as Mg ii, in order to get black hole masses at higher redshifts when Hβ is redshifted out of the optical waveband. However, there is no radius-luminosity relation determined directly from Mg ii. Here, we present an attempt to perform reverberation mapping using Mg ii in the well-studied nearby Seyfert 1 NGC 5548. We used Swift to obtain UV grism spectra of NGC 5548 once every two days from 2013 April to September. Concurrent photometric UV monitoring with Swift provides a well determined continuum light curve that shows strong variability. The Mg ii emission line, however, is not strongly correlated with the continuum variability, and there is no significant lag between the two. We discuss these results in the context of using Mg ii scaling relations to estimate high-redshift black hole masses.