This Letter reports on measurements of the longitudinal polarization fractions in the decays Bd→J/ψK*0 and Bs→J/ψφ using data collected with the Collider Detector at Fermilab. Bd mesons are reconstructed through the decay chain Bd→J/ψK*0, J/ψ→μ+μ−, K*0→K+π−. A sample of 65±10Bd events is used to obtain a longitudinal polarization fraction of γL/γ=0.65±0.10(stat)±0.04(syst). Bs mesons are reconstructed through the decay chain Bs→J/ψφ, J/ψ→μ+μ−, φ→K+K−. A sample of 19±5Bs events is used to obtain the result γL/γ=0.56±0.21(stat)−0.04+0.02(syst).