Watson fell 6-4 6-4 to Elise Mertens and never looked like troubling the Belgian while Broady was swept aside 6-0 5-7 6-1 by Puerto Rico's Monica Puig.
Watson was well beaten in the first set but made a better fist of it in the second only for two poor games in a row to put her behind for the first time, conceding a 5-4 deficit with a horribly hit forehand as her serve collapsed.
The decisive game saw the British number two continue to produce errors at a rate of knots - a shortcoming throughout the match - and having temporarily stemmed the flow of points, she directed a forehand well wide to concede the match.
Broady, who saved match point against former Wimbledon finalist Sabine Lisicki in the previous round, was overwhelmed in the opening set and the second looked destined for a similar outcome as she trailed 3-0, cutting a frustrated figure as her serve also continued to unravel.
The British number three showed tenacity to re-calibrate her sights and, combined with a mini-collapse from Puig, she fought back to win 7-5 only to come unstuck in the decider.
Germany's Carina Witthoeft knocked out the highest seed left in the competition after sweeping aside Kiki Bertens 6-1 6-2.
Bertens was the tournament's second seed but managed to get just 38% of her first serves in play as she was beaten in just 57
Fifth seed Mertens is now the highest ranked player left in the draw and the semi-final line-up is completed by Pauline Parmentier, who crushed Johanna Larsson 6-1 6-2.
Sky Bet can't split Mertens and Puig ahead of their semi-final, betting 10/11 each of two and the other is also considered close, with Parmentier a marginal 5/4 underdog against Witthoeft at 8/13.
Russia's Natalia Vikhlyantseva overcame Alize Cornet of France 4-6 7-5 6-3 and reach the semi-finals of the Kremlin Cup in Moscow.
Vikhlyantseva's last-four opponent is seventh seed Julia Goerges of Germany, who cantered past Lesia Tsurenko of Ukraine 6-4 6-3.
Romania's Irina-Camelia Begu and Daria Kasatkina of Russia will contest the other semi-final, with the latter 1/4 to progress.
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