pompous enough, I think

This is the way this phrase would be translated in American English.

Very similar salutation found online:

"To a Cardinal:
Written Address:
His Eminence, Thomas Cardinal Stand, Archbishop of Los Angeles

Letter Salutation:
Your Eminence

Formal Closing: Be pleased to accept the homage of profound respect with which I have the honor to offer you as,
The humble and dedicated servant of Your Eminence,
(Signature)

[source web reference 1]

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Note added at 18 mins (2010-09-17 12:03:52 GMT)
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Compare:

"la prego* di voler accogliere**, i sensi del mio profondo*** rispetto***"

"be pleased* to accept** the homage of profound*** respect**** with which I have the honor to offer you"

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Note added at 40 mins (2010-09-17 12:25:02 GMT)
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By the way...the phrase I used was taken from 'American' English.

A site titled:

ECCLESIASTICAL FORMS OF ADDRESS FOR CATHOLICS
RECOGNIZED IN THE UNITED STATES

http://www.answerbag.com/q_view/4073#ixzz0zmrUJHGQ

- if you're addressing him by name

Here a cardinal is addressing the Archbishop of Canterbury and jhe just uses "Yours sincerely in Christ"

To His Grace
the Most Reverend and Right Honourable
Dr Rowan Williams
Archbishop of Canterbury

Your Grace, ...
...Yours sincerely in Christ,

Walter Cardinal Kasper
President
http://www.vatican.va/roman_curia/pontifical_councils/chrstu...

Usage in the UK is different from the US, I think, but this is a US site, where it suggests "Yours very truly" - nothing over the top (i.e. not excessively grovelling)
Cardinal
Address: His Eminence, (First and Last Name)
Salutation: Your Eminence: or Dear Cardinal (Surname):
Closing: Yours very truly,
http://www.libraryonline.com/default.asp?pID=63

Siamo solo noi italiani (e i francesi più di noi) ad essere così pomposi! Io non esagererei...
Buon lavoro! ;-)

That's what one is supposed to write according to these websites on 'clergy etiquette'.

http://www.fisheaters.com/addressingclergy.html

'Addressing Clergy in a Letter. When we write to a clergyman (and, by custom, monastics), we should open our letter with the greeting, "Bless, Father." At the end of the letter, it is customary to close with the following line: "Kissing your right hand...." It is not appropriate to invoke a blessing on a clergyman, as many do: "May God bless you." Not only does this show a certain spiritual arrogance before the image of the cleric, but laymen do not have the Grace of the Priesthood and the prerogative to bless in their stead. Even a Priest properly introduces his letters with the words, "The blessing of the Lord" or "May God bless you," rather than offering his own blessing. Though he can do the latter, humility prevails in his behavior, too. Needless to say, when a clergyman writes to his ecclesiastical superior, he should ask for a blessing and not bestow one.'
(source, http://www.orthodoxinfo.com/praxis/clergy_etiquette.aspx)

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Note added at 4 hrs (2010-09-17 16:18:30 GMT)
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I'm sorry, but just couldn't resist adding this

'Cardinal

Direct address: Your Eminence, or Cardinal Hand.
Written address: His Eminence, Thomas Cardinal Hand, Archbishop of Los Angeles, or, His Eminence, The Most Reverend Cardinal Thomas J. Hand, of Los Angeles.
Formal closing: Kissing the Sacred Purple,
Formal introduction: His Eminence, Cardinal of Los Angeles.
Protocol: The same as for a Bishop.
(source, http://www.traditioninaction.org/religious/d003rpHowToAddres...


More seriously (come on, guys), here's what catholics and non-catholics might go for:

'The following are forms of address used by Catholics in letters and in speech. It is perfectly correct for those who are not Catholics to change the conclusion to something such as: "With every good wish to Your Excellency (Eminence, etc.), I am, Sincerely yours, NN.," or even more simply, "With every best wish. Sincerely yours, NN."

CARDINALS:
Addressing a letter: His Eminence (Christian name) Cardinal (Surname) (If an archbishop or bishop give title and see)
Salutation: Your Eminence:
Concluding a letter: <b<Asking the blessing of Your Eminence, I am, Yours respectfully in Christ, N.
In personal speech: Your Eminence
(source, http://www.answerbag.com/q_view/4073. Don't know how authoritative this is. Still, it provides answers, so...)

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Note added at 4 hrs (2010-09-17 16:29:44 GMT)
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Now, you won't believe this, but an alternative to the above is (760,000 ghits, no kidding)

Kissing the sacred purple
http://www.traditioninaction.org/Questions/G004_Deacons.shtm...

But, apparently
'27. In official letters the expressions "kissing the sacred purple" and "kissing the sacred ring" can be omitted.
27. In officiosis litteris scribendis omitti poterunt verba «sacram osculatus purpuram» atque «sacrum anulum osculatus».'
(the Latin version is for you, Maurizio)
(source, http://catholicsites.org/clericaldress/utsivesollicite.html)

Seriously, here's what a good compromise (for catholics and non-catholics) could be:

'The following are forms of address used by Catholics in letters and in speech. It is perfectly correct for those who are not Catholics to change the conclusion to something such as: "With every good wish to Your Excellency (Eminence, etc.), I am, Sincerely yours, NN.," or even more simply, "With every best wish. Sincerely yours, NN."

CARDINALS:
Addressing a letter: His Eminence (Christian name) Cardinal (Surname) (If an archbishop or bishop give title and see)
Salutation: Your Eminence:
Concluding a letter: Asking the blessing of Your Eminence, I am, Yours respectfully in Christ, N.
In personal speech: Your Eminence'
(source, http://www.answerbag.com/q_view/4073)



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Note added at 4 hrs (2010-09-17 16:31:02 GMT)
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Apologies for the mix-up. Don't know what happened there...

While we're offending His Excellency, let's put the fear of suicide bombers into him as well..

... Giuseppe Maria Leccaculo-Bacchettone, Esq.