Westport is located at 36°11'46" North, 96°21'37" West (36.196315, -96.360476).
According to the United States Census Bureau, the town has a total area of 8.45 mi2 (21.89 km2). 3.99 mi2 (10.34 km2) of it is land and 4.46 mi2 (11.55 km2) of it is covered by water. The total area is 52.75% water.
Westport is located in the Central Standard Time (CST) timezone, GMT-06:00. It observes Daylight Saving Time (DST).