The similarities between the relationships in Macbeth and “To His Coy Mistress” is the one person is trying to convince the other. In Macbeth’s case, his wife is trying to convince him to murder the king so he can become king. In the poem, the speaker is trying to convince the mistress to be his lover.
There is a similar relationship in each poem in that one person has influence over the other, or tries to. The genders are switched, of course. In Macbeth the woman is the aggressor, and in “To His Coy Mistress” the man is.
In each case, the pleading party points out that time is of the essence. The speaker begins by telling his mistress they don’t have all the time in the world.
Had we but world enough and time,
This coyness, lady, were no crime.
Lady Macbeth also reminds Macbeth that Duncan is coming soon.
Shall sun that morrow see!
Your face, my Thane, is as a book where men
May read strange matters. To beguile the time,
Look like the time; (Act 1, Scene 5, p. 20)
In each case, the person being pleaded to seems to relent, have a change of mind, and relent. Lady Macbeth has her husband convinced that killing Duncan is in their best interest, but he changes his mind.
Macbeth asks Lady Macbeth if the plan will work.
Will it not be received,
When we have mark'd with blood those sleepy two
Of his own chamber, and used their very daggers,(85)
That they have done't? (Act 1, Scene 5, p. 24)
She tells him they have to be convinced. How could they think otherwise?
In the poem, we only have the speaker’s side of it, but we can infer by his words the lady’s reaction.
Now therefore, while the youthful hue
Sits on thy skin like morning dew,
And while thy willing soul transpires
At every pore with instant fires,
Now let us sport us while we may…
He seems pretty sure he is going to get lucky. Of course, Macbeth relents as well, and kills Duncan.
The main difference is that there are actual back and forth conversations between Lady Macbeth and Macbeth, where in the poem we only hear the speaker's side. We do not really know what the lady is thinking, or if she relents.