  We determine the interface free energy $F_{o.d.}$ between disordered and
ordered phases in the q=10 and q=20 2-d Potts models using the results of
multicanonical Monte Carlo simulations on $L^2$ lattices, and suitable finite
volume estimators. Our results, when extrapolated to the infinite volume limit,
agree to high precision with recent analytical calculations. At the transition
point $\beta_t$ the probability distribution function of the energy exhibits
two maxima. Their locations have $1/L^2$ corrections, in contradiction with
claims of $1/L$ behavior made in the literature. Our data show a flat region
inbetween the two maxima which characterizes two domain configurations.
