Here, Shakespeare simply alludes to heraldic customs.
HAMLET (Act 4, Scene 5)
Laertes describes the hasty funeral of his father:
LAERTES
[...] his obscure funeral--
No trophy, sword, nor hatchment o'er his bones,
No noble rite nor formal ostentation--
KING HENRY VI, PART 2 (Act 5, Scene 1)
Warwick is about to ride in battle and places his crest atop his helmet (Shakespeare errs on the origin of the crest: the Kingmaker inherited it from Sir Richard Beauchamp, 13th Earl of Warwick, his father-in-law).
WARWICK
Now, by my father's badge, old Nevil's crest,
The rampant bear chain'd to the ragged staff,
This day I'll wear aloft my burgonet,
As on a mountain top the cedar shows
That keeps his leaves in spite of any storm,
Even to affright thee with the view thereof.
These are instances where heraldic terms are used as metaphors; in the first cases, this is done in an otherwise unheraldic context, but sometimes the metaphor occurs in a martial context, or the notion of arms as records of honorable deeds serves as the context.
HAMLET (Act 1, Scene 2)
(Horatio describes to Hamlet the ghost he saw, and confirms that his beard was like that of Hamlet's father)
HORATIO
It was, as I have seen it in his life,
A sable silver'd.
A similar metaphor appears in Sonnet 12:
When I behold the violet past prime,
And sable curls all silver'd o'er with white;
A MIDSUMMER NIGHT'S DREAM (Act 3, Scene 2)
Helena recalls her friendship with Hermia, which she thinks has betrayed her. She uses the impaled arms of husband and wife to extend the metaphor of two bodies with one heart as two coats with one crest.
HELENA
So, with two seeming bodies, but one heart;
Two of the first, like coats in heraldry,
Due but to one and crowned with one crest.
HAMLET (Act 2, Scene 2)
Hamlet recalls a passage of a play that particularly struck him; it is Aeneas describing to Dido the fall of Troy. The passage plays on heraldry: the Greek Pyrrhus' arms were black when he was hiding in the Trojan horse, but is now covered with the red blood of whole families, just as a coat of arms tricked by a herald can describe the blood relations of fathers, mothers, daughters, sons.
'The rugged Pyrrhus, he whose sable arms,
Black as his purpose, did the night resemble
When he lay couched in the ominous horse,
Hath now this dread and black complexion smear'd
With heraldry more dismal; head to foot
Now is he total gules; horridly trick'd
With blood of fathers, mothers, daughters, sons, [...]
KING HENRY VI, PART 1 (Act 1, Scene 1)
A messenger warns attendants at Henry V's funeral of recent setbacks in France, which he describes as the cropping of the France quarter in the English royal arms.
Awake, awake, English nobility!
Let not sloth dim your horrors new-begot:
Cropp'd are the flower-de-luces in your arms;
Of England's coat one half is cut away.
KING HENRY VI, PART 2 (Act 4, Scene 10)
Iden has just killed Cade in battle and rejoices.
IDEN
Is't Cade that I have slain, that monstrous traitor?
Sword, I will hollow thee for this thy deed,
And hang thee o'er my tomb when I am dead:
Ne'er shall this blood be wiped from thy point;
But thou shalt wear it as a herald's coat,
To emblaze the honour that thy master got.
THE RAPE OF LUCRECE (204-7)
Tarquin "madly tossed between desire and dread", ponders the shame that will come to him if he follows through on his intentions to rape Lucrece, and how it will be recorded on his coat of arms.
'Yea, though I die, the scandal will survive,
And be an eye-sore in my golden coat;
Some loathsome dash the herald will contrive,
To cipher me how fondly I did dote
THE MERRY WIVES OF WINDSOR (Act 1, Scene 1)
The play begins with Justice Shallow aggrieved by Falstaff and his men; accompanied by his cousin Slender, he explains to Sir Hugh Evans, a Welsh parson, how he will take the matter to the highest court (the Star Chamber), and declines his ranks and titles (including keeper of the rolls, custos rotulorum). Slender then mentions that Shallow is armigerous, and has been so for 300 years (!!), and cites his coat of arms. Evans misunderstands the coat of arms, taking the word "coat" literally and mistaking luce for louse. Another misunderstanding arises over the term heraldic term "quartering." See the pages on the right to bear arms in England for the legal-historical background.
SHALLOW
Sir Hugh, persuade me not; I will make a Star Chamber matter of it. If
he were twenty Sir John Falstaffs, he shall not abuse Robert Shallow, esquire.
SLENDER
In the county of Gloucester, justice of peace and 'Coram.'
SHALLOW
Ay, cousin Slender, and Custa-lorum.
SLENDER
Ay, and Rato-lorum too; and a gentleman born, Master Parson, who writes
himself Armigero, in any bill, warrant, quittance, or obligation,
Armigero.
SHALLOW
Ay, that I do, and have done any time these three hundred years.
SLENDER
All his successors gone before him hath done't; and all his ancestors that
come after him may: they may give the dozen white luces in their
coat.
SHALLOW
It is an old coat.
SIR HUGH EVANS
The dozen white louses do become an old coat well; it agrees well, passant;
it is a familiar beast to man, and signifies love.
SHALLOW
The luce is the fresh fish; the salt fish is an old coat.
SLENDER
I may quarter, coz.
SHALLOW
You may, by marrying.
EVANS
It is marring indeed, if he quarter it.
SHALLOW
Not a whit.
SIR HUGH EVANS
Yes, py'r lady; if he has a quarter of your coat, there is but three skirts
for yourself, in my simple conjectures [...]
In Hamlet (IV,5), Ophelia's madness speech includes the following passage:
There's fennel for you, and columbines: there's rue for you; and here's some for me: we may call it herb-grace o' Sundays: O you must wear your rue with a difference. There's a daisy: I would give you some violets, but they withered all when my father died: they say he made a good end,--
There was an exchange in the Letters to the Editor of the New York Times in April 1994 on this "rue with a difference", whether this was a play on the heraldic meaning of the word "difference" (if so, I don't understand the intent) and whether it might be an allusion to the abortifiacient properties of rue. One instance of rue in heraldry is the collar of the Order of the Thistle in Scotland, which is made of alternating sprigs of thistle and rue. Boutell's Heraldry claims that the words "and rue" are a pun on "Andrew".