We present the results of searches for B decays to charmless two-body final states containing η′ or ω mesons, based on 50.7fb-1of data collected with the BABAR detector. We find the branching fractions B(B+→ η′K+) = (70 ± 8 ± 5) × 10-6, B(B0→ η′K0) = (42+13-11± 4) × 10-6, and B(B+→ ωπ+) = (6.6+2.1-1.8± 0.7) × 10-6, where the first error quoted is statistical and the second is systematic. We give measurements of four additional modes for which the 90% confidence level upper limits are B(B+→ η′π+) < 12 × 10-6, B(B+→ ωK+) < 4 × 10-6, B(B0→ ωK0) < 13 × 10-6, and B(B0→ ωπ0) < 3 × 10-6. © 2001 The American Physical Society.