  Quenched chiral perturbation is used to study the decay constants for
heavy-light mesons beyond the leading order in 1/M. The results are used to
estimate the error in quenched lattice calculations of the decay constants. For
the double ratio $R_1 = ( f_{D_s}/f_D) / (f_{B_s}/f_B)$ we find that the error
is small, conservatively 6%, but likely smaller. We also find that quenching
decreases the ratio $f_{D_s}/f_D$ relative to the unquenched theory.
