The three plaintiffs said they survived a 2012 US drone strike that killed two of their relatives and that the fear of another attack had turned their family lives into "a constant nightmare from which we can't wake up".
However, the Cologne administrative court found that the German government is "under no obligation to prohibit the United States from using the Ramstein Air Base to conduct drone strikes in Yemen".
The court said it agreed that in principle Germany had a duty to protect people against danger to life and limb emanating from its territory.
"In addition, the agreements on the deployment of friendly forces in Germany provide for only very limited influence by German authorities on the use of the properties by foreign troops," a court statement said.
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The court also said the government had repeatedly and recently asked the US "to respect German and international law" in its Ramstein operations and that "the American government has promised to do so".
The plaintiffs, represented by the Berlin-based European Center for Constitutional and Human Rights (ECCHR), had argued that the air base relays signals from US-based operators to the aerial vehicles flying over Yemen.
"See nothing, hear nothing, say nothing -- with this strategy the government cannot and will not be able to meet its obligation to prevent human rights violations committed by the USA via German territory."
The complaint was filed, together with ECCHR and London-based rights group Reprieve, by Yemeni citizens Faisal bin Ali Jaber, Ahmed Saeed bin Ali Jaber and Khaled Mohmed Naser bin Ali Jaber, who did not attend the hearing.