  Recent fully relativistic calculations of radiative rates and electron impact
excitation cross sections for Fe {\sc xiii} are used to generate emission-line
ratios involving 3s$^{2}$3p$^{2}$--3s3p$^{3}$ and
3s$^{2}$3p$^{2}$--3s$^{2}$3p3d transitions in the 170--225 \AA and 235--450 \AA
wavelength ranges covered by the Solar Extreme-Ultraviolet Research Telescope
and Spectrograph (SERTS). A comparison of these line ratios with SERTS active
region observations from rocket flights in 1989 and 1995 reveals generally very
good agreement between theory and experiment. Several new Fe {\sc xiii}
emission features are identified, at wavelengths of 203.79, 259.94, 288.56 and
290.81 \AA. However, major discrepancies between theory and observation remain
for several Fe {\sc xiii} transitions, as previously found by Landi (2002) and
others, which cannot be explained by blending. Errors in the adopted atomic
data appear to be the most likely explanation, in particular for transitions
which have 3s$^{2}$3p3d $^{1}$D$_{2}$ as their upper level. The most useful Fe
{\sc xiii} electron density diagnostics in the SERTS spectral regions are
assessed, in terms of the line pairs involved being (i) apparently free of
atomic physics problems and blends, (ii) close in wavelength to reduce the
effects of possible errors in the instrumental intensity calibration, and (iii)
very sensitive to changes in N$_{e}$ over the range 10$^{8}$--10$^{11}$
cm$^{-3}$. It is concluded that the ratios which best satisfy these conditions
are 200.03/202.04 and 203.17/202.04 for the 170--225 \AA wavelength region, and
348.18/320.80, 348.18/368.16, 359.64/348.18 and 359.83/368.16 for 235--450 \AA.
