  It was recently realized that the three-dimensional O($N$) model possesses an
extraordinary boundary universality class for a finite range of $N \ge 2$. For
a given $N$, the existence and universal properties of this class are predicted
to be controlled by certain amplitudes of the normal universality class, where
one applies an explicit symmetry breaking field to the boundary. In this
Letter, we study the normal universality class for $N = 2, 3$ using Monte Carlo
simulations on an improved lattice model and extract these universal
amplitudes. Our results are in good agreement with direct Monte Carlo studies
of the extraordinary universality class serving as a nontrivial quantitative
check of the connection between the normal and extraordinary classes.
