Using multicanonical Monte Carlo simulations, we have calculated the interface free energy between the coexisting ordered and disordered phase at the temperature driven first-order phase transition of the two-dimensional 7-state Potts model. Our result 2f3= 0.0241±0.0010 is about an order of magnitude smaller than other estimates in the recent literature. We discuss the differences in analysis and give a possible explanation for the discrepancy. Finally, we briefly mention similar investigations at the deconfining phase transition of SU(3) lattice gauge theory.