The 60-year-old TV star is alleged to have harassed the woman despite complaints from her, her husband and the police, a court heard.
McGrath is alleged to have sent his victim electronic messages, approached her in the street, engaged the couple in conversation and sent letters to the victim’s husband.
He appeared at Cambridgeshire Magistrates’ Court in Huntingdon, Cambridgeshire.
Wearing a black coat, green t-shirt and black trousers, he spoke only to confirm his name, address and to enter a not guilty plea to a charge of stalking against a woman.
His alleged victim cannot be named for legal reasons.
McGrath, from Cambridge, is accused of harassing his un-named victim in the city between June last year and August this year.
Prosecutor Anthea Harris said: “It is a stalking offence which continued over a 14-month period, there are a number of aggravating features, these are features which are deliberate and show evidence of pre-planning.”
She added: “The tenure (of the allegations) is striking and distasteful.”
McGrath was granted conditional bail which bans him from contacting the victim or visiting an address in Cambridge.
He is due to stand trial in January.