We present new constraints on the system parameters of the SW Sextantis star DW Ursae Majoris, based on ultraviolet (UV) eclipse observations with the Hubble Space Telescope. Our data were obtained during a low state of the system, in which the UV light was dominated by the hot white dwarf (WD) primary. Eclipse analysis, using the full Roche lobe geometry, allows us to set firm limits on the masses and radii of the system components and the distance between them: 0.67 \leq M_1/M_sun \leq 1.06, 0.008 \leq R_1/R_sun \leq 0.014, M_2/M_sun > 0.16, R_2/R_sun > 0.28 and a/R_sun > 1.05. For q = M_2/M_1 < 1.5 the inclination must satisfy i > 71 degrees. Using Smith & Dhillon's mass-period relation for CV secondaries, our estimates for the system parameters become M_1/M_sun = 0.77 \pm 0.07, R_1/R_sun = 0.012 \pm 0.001, M_2/M_sun = 0.30 \pm 0.10, R_2/R_sun = 0.34 \pm 0.04, q =0.39 \pm 0.12, i = 82 \pm 4 degrees and a/R_sun = 1.14 \pm 0.06. We have also estimated the spectral type of the secondary, M3.5 \pm 1.0, and distance to the system, d =930 \pm 160 pc, from time-resolved I- and K-band photometry. Finally, we have repeated Knigge et al.'s WD model atmosphere fit to the low-state UV spectrum of DW UMa in order to account for the higher surface gravity indicated by our eclipse analysis. In this way we obtained a second estimate for the distance, d = 590 \pm 100 pc, which allows us to obtain a second estimate for the spectral type of the secondary, M7 \pm 2.0. We conclude that the true value for the distance and spectral type will probably be in between the values obtained by the two methods.