Furnished Apartments For Rent In Westport Ct . A 1 bedroom apartment on the average will cost you $2,878 and ranges from $1,525 to $6,500. Find top furnished luxury apartments for rent in westport, ct! 4 Marsh Ct, Westport, CT, 06880 from www.realtor.com 12 furnished luxury apartments for rent in westport, ct. Apartment rent in westport has increased by 22.1% in the past year. 1177 greens farms apartments, westport, ct 06880.