We present new stringent limits on the mass $Mbh$ of the central supermassive black hole for a sample of 7 nearby galaxies. Our $Mbh$ estimates are based on the dynamical modeling of the central width of the nebular emission lines measured over subarcsecond apertures with the Hubble Space Telescope. The central stellar velocity dispersion $sigmac$ of the sample galaxies is derived from new long-slit spectra from ground-based observations and the bulge effective radius is obtained from a two-dimensional photometric decomposition of the i-band images from the Sloan Digital Sky Survey. The derived stringent $Mbh$ limits run parallel and above the $Mbh-sigmac$ relation with no systematic trend depending on the galaxy distance or morphology. This gives further support to previous findings suggesting that the nuclear gravitational potential is remarkably well traced by the width of the nebular lines when the gas is centrally peaked. With our investigation, the number of galaxies with stringent $Mbh$ limits obtained from nebular-line width increases to 114 and can be used for studying the scaling relations between $Mbh$ and properties of their host galaxies.