Laser-selective excitation and optical-absorption techniques have been used to establish comprehensive sets of energy levels for both the ${\mathit{F}}^{\mathrm{\ensuremath{-}}}$ and hydrogenic varieties of the tetragonal symmetry (
C4v) centers in
SrF2 and
CaF2. Polarization of the various spectral lines was used to determine the symmetry labels of many of the energy levels. Reversals of the ordering of some levels between
SrF2 and
CaF2 are found and, in particular, the two lowest levels (
D1 and
D2) of the
1D2 multiplet, which are the originating levels for many of the observed emission transitions, have reversed-symmetry label assignments in
SrF2 and
CaF2. Differences were found between the ground-state Zeeman splittings for the
C4v ${\mathit{F}}^{\mathrm{\ensuremath{-}}}$ and ${\mathit{D}}^{\mathrm{\ensuremath{-}}}$ centers for both
SrF2 and
CaF2. Fluorescence lifetimes of the
C4v hydrogenic centers show a strong dependence on the particular charge-compensating ion present through nonradiative decay processes involving the respective local mode phonons. The upconversion spectra observed for ${\mathit{F}}^{\mathrm{\ensuremath{-}}}$, ${\mathit{T}}^{\mathrm{\ensuremath{-}}}$, and ${\mathit{D}}^{\mathrm{\ensuremath{-}}}$ varieties of the
C4v centers in
SrF2 and for the
C4v ${\mathit{F}}^{\mathrm{\ensuremath{-}}}$ center in
CaF2 are all consistent with excitation of specific subsets of nearby
C4v centers.