Council security measures are being stepped up following the theft of 18 memorial plaques from Bushbury crematorium.
The recent theft, which took place over the weekend of Saturday 11 and Sunday 12 November, follows similar incidents at Bilston and Merridale cemeteries.
Councillor Craig Collingswood, Wolverhampton Council's cabinet member for environment and climate change, said: "I want to assure people that we are committed to doing everything we can to stop crimes such as this and track down the heartless thieves responsible.
This is a deeply upsetting situation for the families involved and we wholeheartedly condemn these appalling thefts.
“Our continued work with police colleagues is resulting in increased patrols and vigilance across the city’s cemeteries, along with the implementation of further security measures to protect our cemeteries.
"We are committed to working hard to bring these heartless robbers to justice and I would urge anyone who has any information which may help apprehend the individuals responsible to contact police via Live Chat or by calling 101 as soon as possible as enquiries continue."