  Measuring broad emission-line widths in active galactic nuclei (AGN) is not
straightforward owing to the complex nature of flux variability in these
systems. Line-width measurements become especially challenging when
signal-to-noise is low, profiles are narrower, or spectral resolution is low.
We conducted an extensive correlation analysis between emission-line
measurements from the optical spectra of Markarian 142 (Mrk 142; a narrow-line
Seyfert galaxy) taken with the Gemini North Telescope (Gemini) at a spectral
resolution of 185.6+\-10.2 km/s and the Lijiang Telescope (LJT) at 695.2+\-3.9
km/s to investigate the disparities in the measured broad-line widths from both
telescope data. Mrk~142 posed a challenge due to its narrow broad-line
profiles, which were severely affected by instrumental broadening in the
lower-resolution LJT spectra. We discovered that allowing the narrow-line flux
of permitted lines having broad and narrow components to vary during spectral
fitting caused a leak in the narrow-line flux to the broad component, resulting
in broader broad-line widths in the LJT spectra. Fixing the narrow-line flux
ratios constrained the flux leak and yielded the Hydrogen-beta broad-line
widths from LJT spectra $\sim$54\% closer to the Gemini Hydrogen-beta widths
than with flexible narrow-line ratios. The availability of spectra at different
resolutions presented this unique opportunity to inspect how spectral
resolution affected emission-line profiles in our data and adopt a unique
method to accurately measure broad-line widths. Reconsidering line-measurement
methods while studying diverse AGN populations is critical for the success of
future reverberation-mapping studies. Based on the technique used in this work,
we offer recommendations for measuring line widths in narrow-line AGN.
