The first is part of an exchange in The Tempest (V, 1) between the wizard Prospero and his daughter Miranda:
MIRANDA: How beauteous mankind is! O brave new world, that has such people in it!Miranda has spent twelve of her fifteen years on the island, and the only humans she can remember seeing before now are her own father and his deformed slave Caliban. It's little wonder that the royal party her father has brought to the island--especially Ferdinand, who Prospero intends will marry her--should dazzle Miranda; nor that her father should have a different perspective, since the party includes two conspirators who deposed him. (Prospero is the rightful Duke of Naples.)
PROSPERO: 'Tis new to thee!
These lines from The Tempest, transported to the beginning of the fourth section of A Kiss Before You Leave Me, stand as an invitation to the reader to examine my Miranda's situation at this point in the novel. She's suddenly a celebrity, of sorts, the model and very public companion of an artist who is... perhaps the flavor of the month, perhaps more. She is, of course, dazzled; even he's dazzled by his success. What she seems not to see, however, is that she forms part of an apparatus that may be elevating him at her expense; moreover, the reader has reasons to question the artist's commitment to her.
The second epigraph from Shakespeare is a line from Measure for Measure (II, 4). Angelo (the strict judge who rules Vienna in the absence of the Duke) has told Isabella, a novice nun who has begged him to spare her brother Claudio's life, that he will do so only in exchange for her virginity. So well established is his reputation for rectitude, he suggests to her, that no one would believe her if she made his offer public.
ANGELO: ...Say what you can, my false o'erweighs your true.One of the ironies of the situation is that the offense for which Angelo has condemned Claudio to death is fornication (Claudio slept with his betrothed wife before the banns had been read a sufficient number of times to give full legal force to their marriage); what Angelo seeks with Isabella is far graver.
The sense of Angelo's line is simple: even if you accuse me truthfully, it is my denial, a lie, that everyone will believe.
The context in the penultimate section of A Kiss Before You Leave Me is quite different. I used the epigraph to focus the reader's attention on one character's claim that might be paraphrased as follows: 'What I told you may technically be a lie, as you see it; but for me, at a deeper level, it is profoundly true.' My intent was dual: to suggest some sort of analogy between the character's ploys and Angelo's, and to ask the reader to weigh the possible truth of that character's claim as paraphrased here.
I apologize for my inability to discuss this more openly; those who've already read A Kiss Before You Leave Me to the end will understand.
Note one thing, though, about both of these epigraphs: they are not intended to pronounce judgement on characters or situations in the novel; rather, they offer different possible perspectives. Think of these lines of dialogue, and all the other epigraphs, as being themselves in dialogue with the novel that quotes them. That, at least, is the approach that works best for me.