They broke into Bilston Cemetery overnight on Wednesday and stole more than 30 bronze plaques, each measuring 24 inches by 18 inches.
The act has been described as "deplorable" and has been condemned by local councillors.
Police have moved to warn scrap metal dealers not to accept any items that are likely to be a result of this theft, or a similar incident last month when more than 50 bronze plaques were stolen from graves at Merridale Cemetery.
Councillor Steve Evans, Wolverhampton Council's cabinet member for city environment and climate change, said: "This is another absolutely deplorable act which we again condemn in the strongest possible terms.
"We are working closely with police and are determined to do all we can to help track down the culprits.
"We are reviewing security measures at all our cemeteries and are also taking the additional precaution of closing certain sites earlier in the evening for a temporary period.
"I would ask anyone who has any information which may help apprehend the individuals responsible for either incident to contact police via livechat or by calling 101 as soon as possible."
Chief Superintendent Richard Fisher, of Wolverhampton Police, added: "We recognise the devastating effects crimes such as these have on grieving family members.
"We are making enquiries to seek to identify the culprits and ask for all our metal recycling and scrap merchants to help us by not accepting any items that are likely to be part of this theft and call us should anyone attend trying to dispose of them.
"We will be passing the message on during visits to our local dealers.
“We ask for the vigilance of our communities and any information to bring the culprits to justice.”
Anyone with information about either incident is asked to contact police via livechat via west-midlands.police.uk/contact-us/live-chat or call 101 and quote crime reference number 20/698472/22 for the Bilston Cemetery theft or crime reference number 20/639096/22 for the Merridale Cemetery theft.