We report the observations of the decays B^+ -> psi(2S)K^+ and B^0
-> psi(2S)K^*(892)^0 in ppbar collisions at a center-of-mass energy of 1.8 TeV
using a 110 pb^-1 data sample recorded by the Collider Detector at Fermilab.
We also construct the decays B^+ -> J/psi K^+ and B^0 -> J/psi K^*(892)^0) and
measure the six ratios of branching fractions of these four decays. The
relative branching-fraction results are shown to be consistent with
phenomeno-logical factorization calculations of hadronic B-meson decays. We
use the world-average branching fraction B(B^+ -> J/psi K^+) to derive B(B^+
-> psi(2S)K^+) = (0.56 +/- 0.08 +/- 0.10) x 10^-3,B(B^0 -> psi(2S)K^*(892)^0)
= (0.92 +\- 0.20 +\- 0.16) x 10^-3, and B(B^0 -> J/psi K^*(892)^0) = (1.78 +/-
0.14 +\- 0.29) x 10^-3, where the first and second uncertainties are
statistical and systematic, respectively.