We present astrometric measurements of 11 nearby ultracool brown dwarfs of spectral types Y and late-T, based on imaging observations from a variety of space-based and ground-based telescopes. These measurements have been used to estimate relative parallaxes and proper motions via maximum likelihood fitting of geometric model curves. To compensate for the modest statistical significance (≲7) of our parallax measurements we have employed a novel Bayesian procedure for distance estimation which makes use of an a priori distribution of tangential velocities, V_tan, assumed similar to that implied by previous observations of T_dwarfs. Our estimated distances are therefore somewhat dependent on that assumption. Nevertheless, the results have yielded distances for five of our eight Y dwarfs and all three T dwarfs. Estimated distances in all cases are ≳ 3 pc. In addition, we have obtained significant estimates of V_tan for two of the Y dwarfs; both are