  We study the most general class of linear boundary-value problems for systems
of $r$-th order ordinary differential equations whose solutions range over the
complex H\"older space $C^{n+r,\alpha}$, with $0\leq n\in\mathbb{Z}$ and
$0<\alpha\leq1$. We prove a constructive criterion under which the solution to
an arbitrary parameter-dependent problem from this class is continuous in
$C^{n+r,\alpha}$ with respect to the parameter. We also prove a two-sided
estimate for the degree of convergence of this solution to the solution of the
corresponding nonperturbed problem.
