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Defending champions Watson and Henri Kontinen beat second seeds Bruno Soares and Elena Vesnina 6-4 6-7 (6-8) 6-3.
Murray and Martina Hingis overcame Marcelo Demoliner and Maria Jose Martinez Sanchez 6-2 7-5.
The number one seeds broke the unseeded pair three times in a one-sided opening set before breaking in the 11th game of the second set en route to victory.
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Watson and Kontinen had 14 chances to break their opponents in the opening set of their match, finally converting one in the ninth game of the first set.
The second set was a tighter affair. Again, the 2016 champions had several opportunities to break, but wasted them before coming unstuck in the tie-break.
However, they took full advantage of their chances in the decider when they broke in the fourth game before going on to secure a second successive appearance in the final.
Heather Watson will face fellow Briton Jamie Murray in Sunday's Wimbledon mixed doubles final.