I inherited some Paragon china.  The set is a rose and floral pattern
on different pastel backgrounds.  The set includes salad/dessert
plates, coffee cups and saucers.  On the back, it says Paragon  H. M.
the Queen & HM Queen Mary-- Fine bone china England--registered.

On the back, it says Paragon  H. M. the Queen & HM Queen Mary-- Fine
bone china England--registered.

Are you sure?

This suggests that H.M. the Queen is paddling her boat, the Queen Mary.

Yes.  I rechecked and that is exactly what it says.

Perhaps Paragon had Royal Warrants from both The Queen and Queen Mary,
The Queen then most probably being the daughter of Queen Mary and
mother of the present Queen.  Queen Mary was "Queen Mother" from 1936
until her death in 1953, but I expect that a Royal Warrant would not
use that title.  Theoretically, if the china was made in the couple of
years after her death, a Royal Warrant in her name might still have
been in effect, and thus "The Queen" could refer to QE II.

I would have thought that reference to Royal Warrants would include
the coat of arms of the person.

Do you know anything about the date of the china?

It appears there are two coats of arms on the back of these dishes.
One on left appears to be two lions and the one on the right appears
to have a lion on the left and an elk or deer with antlers on the
right.  I am not familiar with English royal history or their coats of
arms.  These dishes came into my mother's possession from an estate
sale in the early 1970's.  She later gave them to me.  I am unsure of
the date of origination but have looked through all 800+ offerings on
ebay and find none like them.  The predominate flower is a rose but
there's a large tulip and other flowers as well.

O No Myo

The mother of the present Queen (QEII) was a former Bowes-Lyon; who
married the man who became King George VI.

Queen Mary was the mother of QEII's father

QED

Hi Bryan,

That is what I thought I said  - I won't bather to check - that's what
I meant, and Sandy's descriptions of the "supporters" to the coats of
arms confirm that H M the Queen and H M Queen Mary were respectively
Queen Consort Elizabeth (Bowles-Lyon) and her mother, Queen Consort
Mary (of Teck).

Here is the coat of arms of the then H M the Queen, with two lions:
http://en.wikipedia.org/wiki/Image:QM_Arms.png
You can read about her here:
http://en.wikipedia.org/wiki/Elizabeth_Bowes-Lyon

Here you can read about Queen Mary:
http://en.wikipedia.org/wiki/Mary_of_Teck

If you scroll down quite a bit you will find her standard with the
description of the right hand half, her family's arms "quartered" with
the royal arms as displayed by her grandfather. The Teck arms are
three antlers and three lions, the same as those of the House of
Württemberg in Germany, from which her father   descended.  Teck is a
castle in Germany. I am sure the "supporters" of this coat of arms are
a lion and elk, appropriate to the items on the arms, but I couldn't
find and image of that.

But here at no 22.2621, you will find Mary of Teck.
http://www.btinternet.com/~allan_raymond/Wurttemberg_Royal_Family.htm

So, this all indicates that the china was made between 1936, when
Elizabeth became queen, and 1953, when Mary, her mother died, perhaps
a couple of years later.

But, Sandy, you have asked what the china is worth ... ?
Perhaps localizing its age has a bearing on it value, I don't know.
But interesting  - to me.

Regards, Myoarin

Since you seem to know a lot about this sort of thing, is there a site
on the Internet--or elsewhere--that I might could find the pattern and
find out more of the china's history?  I think the china is beautiful.
 That's why my mother gave them to me. Thanks for your help.

Sandy, 
I was more intrigued by the royalty  - and could have saved myself a
lot of time by first finding this site, that confirms my analysis:
http://www.thepotteries.org/features/paragon1956.htm

This Canadian eBay site has pages of Paragon china.  On pages 2,7, 9
(I believe) I found items that seem to meet your description, but
check out all the pages.
http://pottery.listings.ebay.ca/China-Dinnerware_Paragon_W0QQfsooZ1QQfsopZ1QQsacatZ18883QQsocmdZListingItemList

Here is the US eBay site with more - or the same:
http://listings.ebay.com/China-Dinnerware_Paragon_W0QQfromZwwwQ2egoogleQ2ecomQQsacatZ18883QQsocmdZListingItemListQQssPageNameZVINSQ3a18883

If those don't work, just search with    Paragon china   to find them
and others, such as this one, which may help you identify the name of
your pattern:

http://www.replacements.com/china/PAR.htm

It does not have pictuers for all the names, but it does have lots of prices.
A comparison with those on eBay indicates the spread on prices and the
mark-up of a professional retailer.

I hope that helps.  These are free comments, it's been fun.

Good luck, Myoarin

Dear Myoarin,
    You are a jewel to have invested your time and gone to so much
trouble to assist me.  Thank you so very much.  I can tell you are an
expert at this sort of thing.  This is something I've wanted to
research for a while but didn't really know where to start.  Then I
thought of "Ask Google" and even though they have not responded, I
have gained a world of information through your comments.  I look
forward to reading more about the royalty on the site you mentioned. 
Thanks again.  After years as an RN manager, I recently resigned to
pursue my dream of a small shop of "previously owned treasures." All
the knowledge I can acquire will be of great help in my endeavors.
These dishes, however, are my own treasure and I do not intend to part
with them.  My mother is gone now and they are another precious
connection to her memory.  You are so appreciated.   Sandy

Sandy,
Thank you for the kind words.  Actually, it was easy  - and I went
about it the long way, not very expert.  I happen to know something
about royal warrants, but that can also easily been found on the web.

I wish you success with your shop.

Regards, Myoarin