British number four Watson enjoyed a memorable run to the last 16, her best showing in any grand slam.
But a quarter-final spot proved beyond the 30-year-old from Guernsey as German youngster Niemeier won 6-2 6-4.
Beforehand the crowd were treated to a parade of former champions including Rod Laver, Billie Jean King, Bjorn Borg, Andy Murray and Roger Federer to celebrate Centre Court’s centenary.
Unfortunately, they then got to witness what has been a familiar sight over the last 100 years, that of a British player being knocked out.
Niemeier, 22, may be unseeded but she beat number two seed Anett Kontaveit in the second round, and illustrated her quality with a stunning winner from the baseline as she chased down a Watson lob.
It was a flat first set from Watson, who was broken twice and swatted the net in frustration after missing a simple volley to bring up set point.
Home hopes were briefly raised when Watson confidently broke for a 2-0 lead in the second, but she was unable to back it up and double-faulted as Niemeier hit straight back.
Two more double faults in her next service game spelled the end for Watson as Niemeier wrapped up victory in an hour and 17 minutes.