Adam Clarke on John 21:19

Should glorify God - Ancient writers state that, about thirty-four years after this, Peter was crucified; and that he deemed it so glorious a thing to die for Christ that he begged to be crucified with his head downwards, not considering himself worthy to die in the same posture in which his Lord did. So Eusebius, Prudentius, Chrysostom, and Augustin. See Calmet.

Follow me - Whether our Lord meant by these words that Peter was to walk with him a little way for a private interview, or whether he meant that he was to imitate his example, or be conformed to him in the manner of his death, is very uncertain.