We study the effect of narrowband interference on the error rate of coded multicarrier systems operating over frequency-selective, quasi-static fading channels with non-ideal interleaving. For this purpose we model the interfering signal as a sum of tone interferers, and develop an error-rate estimation method to approximate the performance of the system over each realization of the channel. This method is suitable for obtaining the outage as well as average performance of the system. The analysis is used to quantify the impact of tone interference on the multiband orthogonal frequency division multiplexing (OFDM) proposal for high data-rate ultra-wideband (UWB) communication. The results indicate that tone interference may have a significant impact on multiband OFDM, but that this performance degradation can be mitigated by the use of erasure marking and decoding at the receiver, assuming the receiver can acquire knowledge of the subcarriers impacted by the interfering signal