This paper describes the observation of the decays B^+ ->
psi(2S)K^+ and B^0 -> psi(2S)K^*(892)^0 in 1.8 TeV ppbar collisions and
presents measurements of the branching fractions B(B^+ -> psi(2S)K^+) and
B(B^0 -> psi(2S)K^*(892)^0) relative to B(B^+ -> J/psiK^+) and B(B^0 ->
J/psi K^*(890)^0), respectively.  The psi(2S) mesons are reconstructed in both
the psi(2S) -> mu^+mu^- and psi(2S) -> J/psi pi^+pi^- channels.  The world
average branching fractions for the J/psi channels are used to extract the
absolute branching fractions B(B^+ -> psi(2S)K^+) = (6.8 +/- 1.0(stat.) +/-
1.4(syst.)) x 10^-4 and B(B^0 -> psi(2S)K^*(892)^0) = (9.0 +/- 2.1(stat.) +/-
2.0(syst.)) x 10^-4.