Singapore has been competent, but Taiwan's response has been more impressive.
It's very close to the hot zone, millions of people travel to and from mainland China every year, it has roughly the population of Australia living on 10% of the land Japan has, the WHO refuses any cooperation, and yet there have been under 50 cases and no local transmission.
Not only that, but as a democratic state, Taiwan's control measures have been remarkably measured.
I'd credit two factors:
1) Imposing travel limits three weeks before China even admitted there was an outbreak. After SARS, the TW government had a plan for this epidemic and a healthy skepticism for both official news and the WHO.
2) Taiwan has a relatively high trust society. People generally trust the local CDC and make a genuine effort to take preventative measures, even those primarily for the safety of others. A phone alert is generally all that's needed as a quarantine reminder for those exposed.