Watson, world ranked 110th, was beaten 7-6 (7-2) 6-2 by the Estonian Anett Kontaveit, who is the world number 99.
The 24-year-old faced 18 break points - compared to just one for her opponent - on the way to losing.
World 124 Broady was beaten 6-4 6-2 by German Julia Goerges, who is 46 in the women's rankings.
British pair Heather Watson and Naomi Broady were both knocked out in the first round of the Biel Bienne Open in Switzerland.