  It has been suggested recently ({\it Phys. Rev. Lett.} 91, 232501 (2003))
that the widths of narrow proton resonances are related to neutron Asymptotic
Normalization Coefficients (ANCs) of their bound mirror analogs because of
charge symmetry of nucleon-nucleon interactions.
  This relation is approximated by a simple analytical formula which involves
proton resonance energies, neutron separation energies, charges of residual
nuclei and the range of their strong interaction with the last nucleon. In the
present paper, we perform microscopic-cluster model calculations for the ratio
of proton widths to neutron ANCs squared in mirror states for several light
nuclei. We compare them to predictions of the analytical formula and to
estimates made within a single-particle potential model. A knowledge of this
ratio can be used to predict unknown proton widths for very narrow low-lying
resonances in the neutron-deficient region of the $sd$- and $pf$-shells, which
is important for understanding the nucleosynthesis in the $rp$-process.
