I often confuse 'epigraph' and 'epigram'. These two Greek words seem uncomfortably similar to me.
There's good reason for this: Merriam Webster reveals that 'epigramma' actually derives from the Greek 'epigraphein', meaning 'to write on'. The Roman poet Martial was famed for his 'epigrammata' (epigrams, not epigraphs): witty, terse little poems.
But forget epigrams. I intend to write about the epigraph, by which I mean the little bit of text, often in italics, that sits snugly between the title of a poem and its first line. This is described by MW as 'a quotation set at the beginning of a literary work […] to suggest its theme', which is at best only a partial description of the thing I have in mind.
Has anyone ever been publicly praised for their epigraphs, I wonder? Because currently poets do seem to like them. They're especially fond of prefacing their creations with that troubling wee beast, the 'after' statement. I'm not sure when this started: I've just flicked through The Oxford Book of Twentieth Century English Verse and I can't see any 'after' poems. They all seem to be befores.
Nonetheless, it's not unusual these days to find you're reading something 'After Wendy Cope' or 'After W H Auden'. If there's no mention of a specific poem, we nervously take the 'afters' to be a general allusion to style. Nervously because maybe there's a resemblance between the poem we're about to read and another we ought to know. A resemblance self-evident to everybody except us.
Still, the 'after' statement may be there as a point of honour. Perhaps the poet was inspired by somebody else's poem and wants to acknowledge that fact, whether or not the new poem resembles its 'before' source. (It occurs to me that poets grew keener to acknowledge such influences after poetry plagiarism became a hot topic.)
There are certain risks, though. An 'after' epigraph can make the poet look pompous. I would suggest 'After Seamus Heaney' and 'After William Shakespeare' are best avoided. The same applies to 'For Seamus Heaney' or 'For Philip Larkin'. Besides, writing a poem 'for' a dead poet (as opposed to a living friend) tends to work against the hope that it might have been written for the common reader.
If there is an art involved in the epigraph, shouldn't it be to give the reader a skilful tip-off, something that will make the poem better understood, or more accessible? There might be a painting, for example, that the reader needs to see in order to make sense of the imagery. In today's digital world, the epigraph can be helpfully hyperlinked to a relevant image, recording or film. Or there might be an essential place setting, a location, that the reader needs to know. In such cases, the epigraph is perfectly justified.
When it comes to an 'I. M.' statement, the decision is also straightforward. If a poem's written with a particular person in mind, someone who has perhaps died recently, it can be most helpful, and in some cases essential, to know the piece is 'in memoriam'.
There are even epigraphs consisting simply of a date. An obvious example is 9/11/2001: a historic allusion easily recognised by most adults. Such detail could be vital to making sense of what follows.
And that's the key. If unsure whether to include an epigraph or not, ask yourself whether it offers information the reader can't do without. Are you sure it isn't already in the title? Or the poem itself? You are sure. OK. Then let it stay.
But if the detail is enriching rather than essential, a useful alternative to consider may be a note. For the reader, notes are nicely optional, and can be placed in an obvious position at the foot of the poem-page, or more subtly at the back of the book.
Of course, in certain circumstances you could have an epigram as your epigraph. An epigram might have inspired the whole poem: 'I can resist everything except temptation' (Oscar Wilde). But that would be really confusing.