According to the Wikipedia page on pardons:
In some jurisdictions, accepting such a pardon implicitly constitutes an admission of guilt (see Burdick v. United States in the United States), so in some cases the offer is refused.
A modern example of this is the UK's January 2017 passage of the "Policing and Crime Act 2017", informally known as the "Alan Turing law", which pardoned men convicted under various laws against homosexuality. George Montague was one man convicted under these laws who said he would not accept the pardon.
"To accept a pardon means you accept that you were guilty. I was not guilty of anything. I was only guilty of being in the wrong place at the wrong time," he told BBC Newsnight.
Montague said that he would accept an apology (which I presume would just be a public admission of the government's regret and would not carry any legal weight), but I'm wondering if there is anything legally stronger than a pardon that would not constitute an admission of guilt?