ABSTRACT In this study we present 18$-$24 GHz and high-angular-resolution (0.5 arcsec) radio wavelength Australia Telescope Compact Array follow-up observations towards a sample of 39 HC H ii region candidates. These objects, taken from a sample hosting 6.7 GHz methanol masers, were chosen due to the compact and optically thick nature of their continuum emission. We have detected 27 compact radio sources and constructed their spectral energy distributions over the 5–24 GHz range to determine the young H ii region’s physical properties, i.e. diameter, electron density ${\it n}_{\mbox{e}}$, emission measure, Lyman continuum flux ${\it N}_{\mbox{Ly}}$, and turnover frequency ${\nu }_{\mbox{t}}$. The flux measurements are fitted for 20 objects assuming an ionization-bounded H ii region with uniform density model. For the remaining seven objects that lack constraints spanning both their optically thick and thin regimes, we utilize relations from the literature to determine their physical properties. Comparing these determined parameters with those of known hypercompact (HC) and ultracompact (UC) H ii regions, we have identified 13 HC H ii regions, six intermediate objects that fall between HC H ii and UC H ii regions, six UC H ii regions and one radio jet candidate which increases the known population of HC H ii regions by $\sim$50 per cent. All the young and compact H ii regions are embedded in dusty and dense clumps and $\sim$80 per cent of the HC H ii regions identified in this work are associated with various maser species (CH$_3$OH, H$_2$O, and OH). Four of our radio sources remain optically thick at 24 GHz; we consider these to be among the youngest HC H ii regions.