We describe searches for B meson decays to the charmless vector-vector final states ωK* and ωρ in 89 × 106 BB̄ pairs produced in e+e- annihilation at √s = 10.58 GeV. We measure the following branching fractions in units of 10 -6: B(B0 → ωK*0) = 3.4 -1.6+1.8 ± 0.4(<6.0), B(B+ → ωK*+) = 3.5-2.0+2.5 ± 0.7(<7.4), B(B0 → ωρ0) = 0.6 -1.1+1.3 ± 0.4(<3.3), and B(B+ → ωρ+) = 12.6-3.3+3.7 ± 1.6. The first error quoted is statistical, the second systematic, and the upper limits are defined at 90% confidence level. For B+ → ωρ+ we also measure the longitudinal spin alignment fraction fL = 0.88-0.15+0.12 ± 0.03 and charge asymmetry Ach = (5 ± 26 ± 2)%. © 2005 The American Physical Society.