In 1572 Queen Elizabeth visited as a guest of Charlecote and stopped for two nights
In 1583 Shakespeare visited Charlecote apprehended as a villain

This Oil painting hangs in the library, artist unknown but of the English school. . It is a later 17th century over-painting of a 16th-century panel.
It shows well her jewelled headdress, large lace ruff, richly embroidered skirt and jewelled surcoat. It was bought in 1835; and is on loan from Sir Edmund Fairfax-Lucy

Elizabeth had been doing a Summer Progress to get away from the heat and stench of London and, it was believed, to protect against the plague. She dined at Itchington and then progressed to Warwick Castle to stay for 2 nights with Ambrose Dudley, the earl of Warwick (see mounted photograph) who gave her a large firework display witnessed by the young Shakespeare.
Elizabeth then moved on to Kenilworth for three nights . Kenilworth Castle was owned by her favourite Robert Dudley, Earl of Leicester after which she went back to Warwick for two nights, back again to Kenilworth for five nights and then came to Charlecote for two nights. Robert Dudley had already been to Charlecote seven years earlier when he conferred a knighthood on Thomas Lucy here in this Great Hall. Elizabeth had come to meet her new knight.

My Shakespearean colleagues say they are unaware of Shakespeare witnessing the fireworks although he does seem to have witnessed the elaborate water pageant Robert Dudley laid on for her 1575 visit to Kenilworth (for 19 days) as there are elements of it in both A Midsummer Night’s Dream and Twelfth Night.