<PAGE>

                                                                  EXHIBIT 99.11

                                 Offer of


                            Purchaser Corp. I


                       a Wholly Owned Subsidiary of


                       Northrop Grumman Corporation


            To Exchange Each Outstanding Share Of Common Stock

    (Including Associated Series A Participating Cumulative Preferred Stock
                               Purchase Rights)
                                      of
                        Newport News Shipbuilding Inc.
                                      for
                            Shares of Common Stock
                                      of
                 Northrop Grumman Corporation Valued at $67.50
                                      or
                       $67.50 Net to the Seller in Cash,
      subject, in each case, to the election and proration procedures and

     limitations described in the Prospectus dated November 13, 2001

                and related Letter of Election and Transmittal

 THE OFFER AND WITHDRAWAL RIGHTS WILL EXPIRE AT 12:00 MIDNIGHT, NEW YORK CITY
 TIME, ON THURSDAY NOVEMBER 29, 2001 UNLESS EXTENDED. SHARES TENDERED
 PURSUANT TO THE OFFER MAY BE WITHDRAWN AT ANY TIME PRIOR TO THE EXPIRATION


       OF THE OFFER, BUT NOT DURING ANY SUBSEQUENT OFFERING PERIOD.


                                                         November 13, 2001


To Our Clients:

   Enclosed for your consideration are the Prospectus, dated November 13,
2001, and the related Letter of Election and Transmittal (which, together with
any amendments or supplements thereto, collectively constitute the "Offer") in
connection with the offer by Purchaser Corp. I, a Delaware corporation (the
"Purchaser"), which is a wholly owned subsidiary of Northrop Grumman
Corporation, a Delaware corporation ("Northrop Grumman"), to issue shares of
common stock, par value $1.00 per share (the "Northrop Grumman Shares"),
designed to have a value of $67.50 per share or pay $67.50 per share in cash
(subject, in each case, to the election and proration procedures and
limitations described in the Prospectus and related Letter of Election and
Transmittal) for each outstanding share of common stock, par value $0.01 per
share (the "Common Stock"), of Newport News Shipbuilding Inc., a Delaware
corporation ("Newport News"), including the associated Series A participating
cumulative preferred stock purchase rights issued pursuant to the Newport News
stockholder protection rights agreement (the "Rights" and, together with the
Common Stock, the "Newport News Shares"). Each Newport News stockholder will
be able, subject to proration, to elect to receive cash for all of his or her
Newport News Shares, or Northrop Grumman Shares for all of his or her Newport
News Shares. We are the holder of record of Newport News Shares held for your
account. A tender of such Newport News Shares can be made only by us as the
holder of record and pursuant to your instructions. The enclosed Letter of
Election and Transmittal is furnished to you for your information only and
cannot be used by you to tender Newport News Shares held by us for your
account.


   We request instructions as to whether you wish us to tender any or all of
the Newport News Shares held by us for your account, upon the terms and
subject to the conditions set forth in the Offer.

   Your attention is invited to the following:

   1. The consideration per Newport News Share is either Northrop Grumman
Shares designed to have a value of $67.50 per Newport News share or $67.50 per
Newport News share in cash without interest (subject, in each case, to the
election and proration procedures and limitations described in the Prospectus
and related Letter of Election and Transmittal).

   2. The Offer is being made for all outstanding Newport News Shares.
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   3. The Offer and withdrawal rights will expire at 12:00 midnight, New York
City time, on Thursday, November 29, 2001, unless the Offer is extended.


   4. The Offer is subject to various conditions set forth in the Prospectus,
which you should review in detail.

   5. Any stock transfer taxes applicable to the sale of Newport News Shares
to the Purchaser pursuant to the Offer will be paid by the Purchaser, except
as otherwise provided in Instruction 6 of the Letter of Election and
Transmittal.


   Except as disclosed in the Prospectus, the Purchaser is not aware of any
state in which the making of the Offer is prohibited by administrative or
judicial action pursuant to any valid state statute. In any jurisdiction in
which the securities, blue sky or other laws require the Offer to be made by a
licensed broker or dealer, the Offer will be deemed to be made on behalf of
Northrop Grumman by Salomon Smith Barney, the Dealer Manager for the Offer, or
one or more registered brokers or dealers licensed under the laws of such
jurisdiction.


   If you wish to have us tender any or all of your Newport News Shares,
please so instruct us by completing, executing and returning to us the
instruction form set forth on the reverse side of this letter. An envelope to
return your instructions to us is enclosed. If you authorize the tender of
your Newport News Shares, all such Newport News Shares will be tendered unless
otherwise specified on the reverse side of this letter. Your instructions
should be forwarded to us in sufficient time to permit us to submit a tender
on your behalf prior to the expiration of the Offer.

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<PAGE>

                       INSTRUCTIONS WITH RESPECT TO THE
                               OFFER TO EXCHANGE

                                    OF


                            PURCHASER CORP. I


                       A WHOLLY OWNED SUBSIDIARY OF


                       NORTHROP GRUMMAN CORPORATION

                    EACH OUTSTANDING SHARE OF COMMON STOCK
    (INCLUDING ASSOCIATED SERIES A PARTICIPATING CUMULATIVE PREFERRED STOCK
                               PURCHASE RIGHTS)
                                      OF
                        NEWPORT NEWS SHIPBUILDING INC.
                                      FOR
                            SHARES OF COMMON STOCK
                                      OF
                 NORTHROP GRUMMAN CORPORATION VALUED AT $67.50
                                      OR

 $67.50 NET TO THE SELLER IN CASH, SUBJECT, IN EACH CASE, TO THE ELECTION AND
    PRORATION PROCEDURES AND LIMITATIONS DESCRIBED IN THE PROSPECTUS DATED
     NOVEMBER 13, 2001 AND RELATED LETTER OF ELECTION AND TRANSMITTAL


   The undersigned acknowledge(s) receipt of your letter and the enclosed
Prospectus dated November 13, 2001 and the related Letter of Election and
Transmittal in connection with the Offer by Purchaser Corp. I, a Delaware
corporation (the "Purchaser"), which is a wholly owned subsidiary of Northrop
Grumman Corporation, a Delaware corporation, to issue shares of common stock,
par value $1.00 per share (the "Northrop Grumman Shares"), designed to have a
value of $67.50 per Newport News share or pay $67.50 per Newport News share in
cash (subject, in each case, to the election and proration procedures and
limitations described in the Prospectus and related Letter of Election and
Transmittal) for each outstanding share of common stock, par value $0.01 per
share (the "Common Stock"), of Newport News Shipbuilding Inc., a Delaware
corporation ("Newport News"), including the associated Series A participating
cumulative preferred stock purchase rights issued pursuant to the Newport News
stockholder protection rights agreement (the "Rights" and, together with the
Common Stock, the "Newport News Shares"). You will be able, subject to
proration, to elect to receive cash for all of your Newport News Shares, or
Northrop Grumman Shares for all of your Newport News Shares.


   This will instruct you to tender to the Purchaser the number of Newport
News Shares indicated below (or if no number is indicated below, all Newport
News Shares) that are held by you for the account of the undersigned and to
make the following elections in respect of such Newport News Shares, upon the
terms and subject to the conditions set forth in the Offer.


Number of Newport News Shares to be Tendered:*
-----------------------------------------------------------------

[_]Check here if you are electing to receive cash for your Newport News
Shares.

[_]Check here if you are electing to receive Northrop Grumman Shares for your
Newport News Shares.

[_]Check here if you are not making any election with respect to your Newport
News Shares.

Total Number of Newport News Shares held by you:
-----------------------------------------------------------------

                                            Date: ______________________ , 2001

                                            -----------------------------------
                                            Signature(s)
                                            -----------------------------------
                                            Print Name(s)
                                            -----------------------------------
                                            Print Address(es)
                                            -----------------------------------
                                            Area Code and Telephone Number
                                            -----------------------------------
                                            Tax ID or Social Security Number

 * Unless otherwise indicated, it will be assumed that all Newport News Shares
   held by us for your account are to be tendered.

  Stockholders are required to make the same election of all Newport News
  Shares tendered pursuant to a single instruction form. Stockholders who
  desire to make a cash election for a portion of their Newport News Shares
  and a Northrop Grumman stock election for their remaining shares must
  complete an additional instruction form.


                   PLEASE RETURN THIS FORM TO THE BROKERAGE
                         FIRM MAINTAINING YOUR ACCOUNT

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