Conant is happily married to Scott Conant, who is the son of Anne Anne (Varrone) Conant and Charles Conant. After several years of dating, the pair exchanged wedding vows in the year 2007.
Their wedding took place in the Turkish town of Bodrum. Scott was married for the second time, while Meltem was married for the first time.
They spent their honeymoon in Tahiti, French Polynesia’s largest island. The couple has been together for 13 years and has developed a close relationship over that period.