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 the signal-to-noise ratio 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(-1) and the Lijiang Telescope (LJT) at 695.2 +/- 3.9 km s(-1) to investigate the disparities in the measured broad-line widths from both telescopes' data. Due to its narrow broad-line profiles, which were severely affected by instrumental broadening in the lower-resolution LJT spectra, Mrk 142 posed a challenge. 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 H beta broad-line widths from LJT spectra similar to 54% closer to the Gemini H 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.