New calculations of radiative rates and electron impact excitation cross sections for Fe XI are used to derive emission-line intensity ratios involving 3s23p4-3s23p33d transitions in the 180-223 A wavelength range. These ratios are subsequently compared with observations of a solar active region obtained during the 1995 flight of the Solar Extreme Ultraviolet Research Telescope and Spectrograph (SERTS). The version of SERTS flown in 1995 incorporated a multilayer grating that enhanced the instrumental sensitivity for features in the ~170-225 A wavelength range, observed in second order between 340 and 450 A. This enhancement led to the detection of many emission lines not seen on previous SERTS flights, which were measured with the highest spectral resolution (0.03 A) ever achieved for spatially resolved active region spectra in this wavelength range. However, even at this high spectral resolution, several of the Fe XI lines are found to be blended, although the sources of the blends are identified in the majority of cases. The most useful Fe XI electron density diagnostic line intensity ratio is I(184.80 A)/I(188.21 A). This ratio involves lines close in wavelength and free from blends, and it varies by a factor of 11.7 between Ne = 109 and 1011 cm-3 yet shows little temperature sensitivity. An unknown line in the SERTS spectrum at 189.00 A is found to be due to Fe XI, the first time (to our knowledge) this feature has been identified in the solar spectrum. Similarly, there are new identifications of the Fe XI 192.88, 198.56, and 202.42 A features, although the latter two are blended with S VIII/Fe XII and Fe XIII, respectively.