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                                                                     Exhibit 4.2



                               WARRANT AGREEMENT

                         Dated as of January 12, 2000


                                 By and among



                             DIGEX, INCORPORATED,


                             MICROSOFT CORPORATION

                                      and

                              CPQ HOLDINGS, INC.
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          WARRANT AGREEMENT dated as of January 12, 2000 by and among DIGEX,
INCORPORATED, a Delaware corporation (the "Company"), Microsoft Corporation, a
Delaware corporation, and CPQ Holdings, Inc., a Delaware corporation (Microsoft
Corporation and CPQ Holdings, Inc. together, the "Initial Holders").

          NOW, THEREFORE, the parties hereto hereby agree as follows:

          1.  Grant.  The Company hereby grants to the Initial Holders, in the
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amounts set forth in Exhibit A opposite their names, warrants ("Warrants") which
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shall entitle the registered holder thereof to purchase from the Company, at any
time or from time to time hereafter until 5:00 P.M., New York time, on January
12, 2003 (the "Expiration Date"), up to 1,065,000 shares (the "Warrant Shares")
of Class A Common Stock, par value $.01 per share, of the Company ("Common
Stock"), subject to adjustment as provided in Section 6, at the exercise price
of $57.00 per share, subject to adjustment as provided in Section 6 (the
"Exercise Price"), all subject to the terms and upon the conditions set forth
herein.  Each Warrant not exercised or deemed exercised on or prior to the
Expiration Date shall become invalid and all rights thereunder, and all rights
in respect thereof under this Agreement, shall cease as of that time.

          2.  Warrant Certificates.  The Warrants shall be evidenced by
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certificates issued pursuant to this Agreement (the "Warrant Certificates") in
the form set forth in Exhibit B hereto, with such appropriate insertions,
                      ---------
omissions, substitutions, and other variations as are required or permitted by
this Agreement.

          3.  Exercise of Warrant.
              -------------------

          (a) General.  Subject to the provisions of this Agreement, upon
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surrender to Continental Transfer & Trust Company (the "Transfer Agent") at its
principal office of a Warrant Certificate with the annexed Form of Election to
Purchase duly executed, together with Payment (as defined below) of the Exercise
Price then in effect, the Transfer Agent shall issue and deliver promptly to the
registered holder of such Warrant Certificate, a certificate or certificates for
the Warrant Shares or other securities or property to which the registered
holder is entitled, registered in the name of such registered holder or, upon
the written order of such registered holder, in such name or names as such
registered holder may designate.  Any certificate or certificates representing
Warrant Shares shall be deemed to have been issued and any person so designated
to be named therein shall be deemed to have become the holder of record of the
Warrant Shares as of the date of the surrender of such Warrant Certificate
(together with such duly executed Form of Election to Purchase) and Payment of
the Exercise Price.

          (b) Payment.    Payment of the Exercise Price shall not be made in
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cash.  Each registered holder of the Warrants shall exercise its rights to
receive Warrant Shares on a net basis, such that without the exchange of any
funds, such holder receives that number of Warrant Shares that would otherwise
be issuable upon a cash exercise of such Warrants less that number of Warrant
Shares having a current market price equal to the aggregate cash Exercise Price
that

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would otherwise have been paid by such holder for the number of Warrant Shares
with respect to which such Warrant is being exercised. For purposes of this
Warrant Agreement, "Payment" of the Exercise Price shall be made pursuant to the
previous sentence.

          For the purpose of any computation under this paragraph 3(b), the
current market price per share of Common Stock on any day shall be deemed to be
the average of the Closing Prices of the Common Stock for the 10 consecutive
trading days ending on the day before the day the Warrant Certificate (together
with a duly executed Form of Election to Purchase) is delivered to the Company.
The term "Closing Price" shall mean, for each trading day, the last reported
sale price on the Nasdaq National Market or, if the Common Stock is not quoted
on the Nasdaq National Market, the average of the closing bid and asked prices
in the over-the-counter market as furnished by any New York Stock Exchange
member firm selected from time to time by the Company for that purpose.  If for
any reason the current market price per share cannot be determined pursuant to
the foregoing provisions of this paragraph, the current market price per share
shall be the fair market value thereof as determined in good faith by the Board
of Directors of the Company (the "Board").

          (c)  Exercise in Whole or in Part.  The purchase rights evidenced by a
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Warrant Certificate shall be exercisable, at the election of the registered
holder thereof, in whole or in part, but only for lots of 100 (as appropriately
adjusted for any reverse stock splits and similar transactions that result in
fewer Warrant Shares issuable upon exercise) Warrant Shares or integral
multiples thereof if less than all the Warrants then held by such registered
holder are being exercised. If less than all of the Warrant Shares purchasable
under any Warrant Certificate are purchased, the Transfer Agent shall cancel
such Warrant Certificate upon the surrender thereof and shall execute and
deliver a new Warrant Certificate of like tenor for the remaining number of
Warrant Shares purchasable thereunder.

          (d)  Fractional Shares.  No fractional shares of Common Stock shall be
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issued upon exercise of any Warrants. Instead the Transfer Agent shall round the
results of an exercise up to the nearest full share of Common Stock.

          (e)  Reservation of Shares.  The Company has reserved and deposited in
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escrow with the Transfer Agent enough shares of Common Stock to permit the
exercise of the Warrants in full. From time to time, upon any adjustment of the
Exercise Price and the number of Warrant Shares deliverable hereunder pursuant
to Section 6, the Company shall reserve and deposit in escrow with the Transfer
Agent enough additional shares of Common Stock to permit the exercise of the
Warrants in full, as so adjusted. All such shares of Common Stock held by the
Transfer Agent in escrow shall not be deemed outstanding until delivered by the
Transfer Agent to a registered holder of the Warrants pursuant to the terms
hereof. All shares of Common Stock that may be issued to a registered holder of
the Warrants upon exercise shall be fully paid and nonassessable and free of all
taxes, liens and charges in respect thereof other than those resulting from any
action taken by the registered holder or as provided in Section 8 hereof. The

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Company shall endeavor to comply with all securities laws regulating the offer
and delivery of shares of Common Stock upon exercise of the Warrants.

          4.  Restrictions on Transfer.
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          (a)  Warrant Register.  The Transfer Agent shall maintain at its
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principal office a Warrant Register for registration of the Warrants and Warrant
Certificates and transfers thereof.  The Transfer Agent shall initially register
the outstanding Warrants in the name of the Initial Holders.  The Transfer Agent
may deem and treat the registered holder(s) of the Warrant Certificates as the
absolute owner(s) thereof and of the Warrants represented thereby
(notwithstanding any notation of ownership or other writing on the Warrant
Certificates made by any person) for the purpose of any exercise thereof or any
distribution to the holder(s) thereof, and for all other purposes, and neither
the Company nor the Transfer Agent shall be affected by any notice to the
contrary.

          (b)  Warrants and Warrant Shares Not Registered.  Each registered
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holder of the Warrants, by acceptance thereof, represents and acknowledges that
the Warrants and the Warrant Shares which may be purchased upon exercise of a
Warrant are not registered under the Securities Act of 1933, as amended (the
"Securities Act"), that the issuance of the Warrants and the offering and sale
of such Warrant Shares are being made in reliance on the exemption from
registration under Section 4(2) of the Securities Act as not involving any
public offering and that the Company's reliance on such exemption is predicated
in part on the representations made by the Initial Holders of the Warrants to
and with the Company that each such holder (1) is acquiring the Warrants for
investment for its own account, with no present intention of reselling or
otherwise distributing the same, (2) is an "accredited investor" as defined in
Regulation D under the Securities Act, and (3) has such knowledge and experience
in financial and business matters that it is capable of evaluating the merits
and risks of the investments made or to be made in connection with the
acquisition and exercise of the Warrants. Neither the Warrants nor the related
Warrant Shares may be transferred except (i) pursuant to an effective
registration statement under the Securities Act, or (ii) if such transferee
makes the applicable representations set forth in the preceding sentence in
writing to the Company, with the delivery to the Company and the Transfer Agent
of an opinion of counsel, reasonably satisfactory to the Company, stating that
(A) no registration is required under the Securities Act, and (B) such
disposition will also be in compliance with applicable state securities law;
provided that no such opinion of counsel shall be required for a transfer of the
Warrants or the related Warrant Shares by an Initial Holder to any of its
affiliates, provided that such affiliate assumes all of such Initial Holder's
obligations hereunder.

          (c)  Notice and Registration of Transfer.  Each registered holder
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of the Warrants, by acceptance thereof, agrees that prior to any disposition by
such holder of the Warrants or of any Warrant Shares, such holder will give
written notice to the Transfer Agent expressing such holder's intention to
effect such disposition and describing briefly such holder's intention as to the
manner in which the Warrants or the Warrant Shares theretofore issued or

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thereafter issuable upon exercise hereof, are to be disposed of together with
the opinion, if any, required by paragraph 4(b) above, whereupon, but only if
such transfer is permitted pursuant to paragraph 4(b) above, such transferring
holder shall be entitled to dispose of the Warrants and/or the Warrant Shares
theretofore issued upon the exercise thereof, all in accordance with the terms
of the notice delivered by such holder to the Transfer Agent.  In the event of
such transfer, the Transfer Agent shall register the transfer of any outstanding
Warrants in the Warrant Register upon surrender of the Warrant Certificate(s)
evidencing such Warrants to the Transfer Agent at its principal office,
accompanied by a written instrument of transfer in form satisfactory to it, duly
executed by the registered holder thereof.   Upon any such registration or
transfer, new Warrant Certificate(s) evidencing such transferred Warrants shall
be issued to the transferee(s) and the surrendered Warrant Certificate(s) shall
be canceled.

          5.  Special Agreements of the Company.  The Company covenants and
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agrees as follows:

          (a) Listing on Securities Exchanges.  If the Common Stock is listed on
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a stock exchange, the Company will use its reasonable best efforts to procure at
its sole expense the listing of all Warrant Shares (subject to issuance or
notice of issuance) on all stock exchanges on which the Common Stock is then
listed and maintain the listing of such shares and other securities after
issuance.

          (b) Actions in Avoidance; Non-Dilution.  The Company will not,
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by amendment of its Restated Certificate of Incorporation, as amended, or
through any reorganization, transfer of assets, consolidation, merger, issue or
sale of securities or otherwise, avoid or take any action which would have the
effect of avoiding the observance or performance of any of the terms to be
observed or performed hereunder by the Company but will at all times in good
faith assist in carrying out all of the provisions of the Warrants and in taking
all of such action as may be necessary or appropriate in order to protect the
rights of the registered holders of the Warrants against impairment.

          6.  Adjustment of Exercise Price and Number of Warrant Shares
              ---------------------------------------------------------
Issuable. The number and kind of shares purchasable upon the exercise of
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Warrants and the Exercise Price shall be subject to adjustment from time to time
as follows:

          (a) In case the Company shall pay or make a dividend or other
distribution on any class of capital stock of the Company in Common Stock, the
Exercise Price in effect at the opening of business on the day following the
date fixed for the determination of stockholders entitled to receive such
dividend or other distribution shall be reduced by multiplying such Exercise
Price by a fraction the numerator of which shall be the number of shares of
Common Stock outstanding at the close of business on the date fixed for such
determination and the denominator of which shall be the sum of such number of
shares and the total number shares constituting such dividend or other
distribution, such reduction to become effective immediately after the opening
of business on the day following the date fixed for such determination of the

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holders entitled to such dividends and distributions.  For the purposes of this
paragraph 6(a), the number of shares of Common Stock at any time outstanding
shall not include shares held in the treasury of the Company.  The Company will
not pay any dividend or make any distribution on shares of Common Stock held in
the treasury of the Company.

          (b) In case the Company shall issue Common Stock, any security
convertible into or exercisable for Common Stock, or rights, options or warrants
to subscribe for, purchase or acquire shares of Common Stock or other securities
convertible into or exercisable for Common Stock (excluding shares issued (i) in
any of the transactions described in paragraphs 6(a), 6(c) or 6(d) of this
Agreement, (ii) pursuant to the Company's employee incentive plans, (iii) upon
exercise of options and warrants of the Company outstanding as of the date
hereof, (iv) to shareholders of any corporation which merges into the Company or
a subsidiary of the Company in proportion to their stock holdings of such
corporation immediately prior to such merger, upon such merger, (v) upon
conversion or exchange of any preferred stock or convertible debt of the
Company, or (vi) in a bona fide offering (whether pursuant to a registered
offering or an offering pursuant to Rule 144A of the Securities Act) pursuant to
a firm commitment underwriting designed to achieve a broad distribution and in
which no person (or group of affiliated persons) has a prior arrangement to
acquire shares in the offering such that, after giving effect to the offering,
such person or group would beneficially own shares representing 5% or more of
the total shares outstanding), at a price per share (on an as converted or
exercised basis) less than the current market price per share (determined as
provided in paragraph 6(f) below) of the Common Stock on the  earliest of (x)
the date of the closing of any new issuance, (y) the date fixed for the
determination of stockholders entitled to receive such securities, and (z) the
date on which the Company becomes contractually obligated to issue such
securities, the Exercise Price in effect at the opening of business on the day
following the date fixed for such determination shall be reduced by multiplying
such Exercise Price by a fraction the numerator of which shall be the number of
shares of Common Stock outstanding at the close of business on the date fixed
for such determination plus the number of shares of Common Stock which the
aggregate offering price for the total number of shares of Common Stock so
offered for subscription, purchase or acquisition would purchase at such current
market price per share and the denominator of which shall be the number of
shares of Common Stock outstanding at the close of business on the date fixed
for such determination plus the number of shares of Common Stock so offered for
subscription, purchase or acquisition, such reduction to become effective
immediately after the opening of business on the day following the date fixed
for such determination of the holders entitled to such rights, options or
warrants.  However, upon the expiration of any right, option or warrant to
purchase Common Stock, the issuance of which resulted in an adjustment in the
Exercise Price pursuant to this paragraph 6(b), if any such right, option or
warrant shall expire and shall not have been exercised, the Exercise Price shall
be recomputed immediately upon such expiration and effective immediately upon
such expiration shall be increased to the price it would have been (but
reflecting any other adjustments to the Exercise Price made pursuant to the
provisions of this paragraph 6 after the issuance of such rights, options or
warrants) had the adjustment of the Exercise Price made upon the issuance of
such rights, options or warrants been made on the basis of offering for
subscription or purchase only that number of shares of

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Common Stock actually purchased upon the exercise of such rights, options or
warrants. No further adjustment shall be made upon exercise of any right, option
or warrant if any adjustment shall have been made upon the issuance of such
security. For the purposes of this paragraph 6(b), the number of shares of
Common Stock at any time outstanding shall not include shares held in the
treasury of the Company. The Company will not issue any rights, options or
warrants in respect of shares of Common Stock held in the treasury of the
Company.

          (c) In case the outstanding shares of Common Stock shall be subdivided
into a greater number of shares of Common Stock, the Exercise Price in effect at
the opening of business on the day following the day upon which such subdivision
becomes effective shall be reduced, and, conversely, in case the outstanding
shares of Common Stock shall each be combined into a smaller number of shares of
Common Stock, the Exercise Price in effect at the opening of business on the day
following the day upon which such combination becomes effective shall be
increased to equal the product of (x) the Exercise Price in effect on such date
and (y) a fraction the numerator of which shall be the number of shares of
Common Stock outstanding immediately prior to such subdivision or combination,
as the case may be, and the denominator of which shall be the number of shares
of Common Stock outstanding immediately after such subdivision or combination,
as the case may be.  Such reduction or increase, as the case may be, shall
become effective immediately after the opening of business on the day following
the day upon which such subdivision or combination becomes effective.

          (d) In case the Company shall, by dividend or otherwise, distribute to
all holders of its Common Stock (A) evidences of its indebtedness or (B) shares
of any class of capital stock, cash or other assets (including securities, but
excluding (x) any rights, options or warrants for which an adjustment has been
made under paragraph 6(b) above, (y) any dividend or distribution for which an
adjustment has been made under paragraph 6(a) or 6(c) above, and (z) cash
dividends paid from the Company's retained earnings, unless the sum of (1) all
such cash dividends and distributions made within the preceding 12 months in
respect of which no adjustment has been made and (2) any cash and the fair
market value of other consideration paid in respect of any repurchases of Common
Stock by the Company or any of its subsidiaries within the preceding 12 months
in respect of which no adjustment has been made, exceeds 20% of the Company's
market capitalization (being the product of the then current market price per
share (determined as provided in paragraph 6(f) below) of the Common Stock times
the aggregate number of shares of Common Stock then outstanding on the record
date for such distribution)), then in each case, the Exercise Price in effect at
the opening of business on the day following the date fixed for the
determination of holders of Common Stock entitled to receive such distribution
shall be adjusted by multiplying such Exercise Price by a fraction of which the
numerator shall be the current market price per share (determined as provided in
paragraph 6(f) below) of the Common Stock on such date of determination less the
then fair market value as determined by the Board (whose determination shall be
conclusive) of the portion of the capital stock, cash or other assets or
evidences of indebtedness so distributed (and for which an adjustment to the
Exercise Price has not previously been made pursuant to the terms of this
paragraph 6) applicable to one share of Common Stock, and the denominator shall
be such current market price per share

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of the Common Stock, such adjustment to become effective immediately after the
opening of business on the day following such date of determination of the
holders entitled to such distribution. The following transactions shall be
excluded from the foregoing clauses (1) and (2): repurchases of Common Stock
issued under the Company's stock incentive programs in accordance with the
provisions thereof.

          (e) In the case of any reclassification or change of the capital stock
of the Company, upon consummation of such reclassification or change, each
Warrant shall survive such reclassification or change and automatically become
exercisable into the kind and amount of securities, cash or other property
receivable upon such reclassification or change by a holder of the number of
shares of Common Stock into which such Warrant might have been exercised
immediately prior to such reclassification or change.  Appropriate adjustment
(as determined by the Board) shall be made in the application of the provisions
set forth herein with respect to the rights and interests thereafter of the
holders of the Warrants, to the end that the provisions set forth herein
(including the provisions with respect to changes in and other adjustment of the
Exercise Price) shall thereafter be applicable, as nearly as reasonably may be,
in relation to any shares of stock or other securities or property thereafter
deliverable upon exercise of the Warrants.

          (f) For the purpose of any computation under paragraph 6(b) or 6(d)
above, the current market price per share of Common Stock on any day shall be
deemed to be the average of the Closing Prices of the Common Stock for the 20
consecutive trading days ending  the day before the day in question; provided
that, in the case of paragraph 6(d), if the period between the date of the
public announcement of the dividend or distribution and the date for the
determination of holders of Common Stock entitled to receive such dividend or
distribution shall be less than 20 trading days, the period shall be such lesser
number of trading days but, in any event, not less than five trading days.

          (g)  No adjustment in the Exercise Price need be made until all
cumulative adjustments amount to 1% or more of the Exercise Price as last
adjusted.  Any adjustments that are not made shall be carried forward and taken
into account in any subsequent adjustment.  All calculations under this
paragraph 6 shall be made to the nearest 1/1,000th of a cent or to the nearest
1/1,000th of a share, as the case may be.

          (h)  For purposes of this paragraph 6, "Common Stock" includes any
stock of any  class of the Company which has no preference in respect of
dividends or of amounts payable in the event of any voluntary or involuntary
liquidation, dissolution or winding-up of the Company and which is not subject
to redemption by the Company (including Class A Common Stock, par value $.01 per
share, and Class B Common Stock, par value $.01 per share, of the Company).
However, subject to the provisions of paragraph 6(l) below, shares issuable on
exercise of the Warrants shall include only shares of the class designated as
Class A Common Stock of the Company on the date hereof or shares of any class or
classes or other securities or assets resulting from any reclassification
thereof; provided that, if at any time there shall be more than one such

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resulting class, the shares of each such class then so issuable shall be
substantially in the proportion which the total number of shares of such class
resulting from all such reclassifications bears to the total number of shares of
all such classes resulting from all such reclassifications.

          (i) No adjustment in the Exercise Price shall reduce the Exercise
Price below the then par value of the Common Stock.  No adjustment in the
Exercise Price need be made under paragraphs 6(a), 6(b) and 6(d) above if the
Company issues or distributes to each registered holder of Warrants the shares
of Common Stock, evidences of indebtedness, assets, rights, options or warrants
referred to in those paragraphs which each registered holder would have been
entitled to receive had the Warrants been exercised prior to the happening of
such event or the record date with respect thereto.

          (j) Whenever the Exercise Price is adjusted pursuant to paragraphs
6(a), 6(b), 6(c) or 6(d) above, (A) the number of Warrant Shares purchasable
upon exercise of any Warrant shall be adjusted by multiplying such number of
Warrant Shares by a fraction the numerator of which is the Exercise Price
immediately prior to such adjustment and the denominator of which is the
Exercise Price immediately after such adjustment and (B) the Company shall
promptly mail to registered holders of Warrants, first class, postage prepaid, a
notice of the adjustment together with a certificate from the Company's
independent public accountants briefly stating the facts requiring the
adjustment and the manner of computing it.  The certificate shall be conclusive
evidence that the adjustment is correct.

          (k)  If:

          (A) the Company takes any action which would require an adjustment in
the Exercise Price pursuant to this Section 6;

          (B) a capital reorganization of the Company occurs or the Company
consolidates or merges with, or transfers all or substantially all of its assets
to, another corporation,; or

          (C) there is a dissolution or liquidation of the Company;

the Company shall mail to registered holders of the Warrants, first class,
postage prepaid, a notice stating the proposed record or effective date, as the
case may be.  The Company shall mail the notice at least 5 days before such
proposed record or effective date.  However, failure to mail the notice or any
defect in it shall not affect the validity of any transaction referred to in
clause (A), (B) or (C) of this paragraph 6(k).

          (l) In the case of any consolidation of the Company or merger of the
Company with any other entity or the sale or transfer of all or substantially
all the assets of the Company pursuant to which the Company's Common Stock is
converted into other securities, cash or assets, upon consummation of such
transaction, each Warrant shall survive such merger

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or sale and automatically become exercisable into the kind and amount of
securities, cash or other assets receivable upon the consolidation, merger, sale
or transfer by a holder of the number of shares of Common Stock into which such
Warrant might have been exercised immediately prior to such consolidation,
merger, transfer or sale (assuming such holder of Common Stock failed to
exercise any rights of election and received per share the kind and amount of
consideration receivable per share by a plurality of non-electing shares).
Appropriate adjustment (as determined by the Board) shall be made in the
application of the provisions herein set forth with respect to the rights and
interests thereafter of the holders of Warrants, to the end that the provisions
set forth herein (including provisions with respect to changes in and other
adjustment of the Exercise Price) shall thereafter be applicable, as nearly as
reasonably may be, in relation to any shares of stock or other securities or
property thereafter deliverable upon the exercise of Warrants. If this paragraph
6(l) applies, paragraphs 6(a), 6(c) and 6(e) do not apply.

          (m) In any case in which this paragraph 6 shall require that an
adjustment as a result of any event become effective from and after a record
date, the Company may elect to defer until after the occurrence of such event
the issuance to the holder of any Warrants exercised after such record date and
before the occurrence of such event of the additional shares of Common Stock
issuable upon such exercise over and above the shares issuable on the basis of
the Exercise Price and number of Warrant Shares in effect immediately prior to
adjustment; provided, however, that if such event shall not have occurred and
authorization of such event shall be rescinded by the Company, the Exercise
Price and number of Warrant Shares shall be recomputed immediately upon such
rescission to the price that would have been in effect had such event not been
authorized, provided that such rescission is permitted by and effective under
applicable laws.

          7.  Exchange and Replacement of Warrant Certificates.  Each Warrant
              ------------------------------------------------
Certificate is exchangeable without expense, upon the surrender thereof by the
registered holder thereof at the principal executive office of the Transfer
Agent, for a new Warrant Certificate of like tenor and date representing in the
aggregate the right to purchase the same number of Warrant Shares in such
denominations as shall be designated by the registered holder thereof at the
time of such surrender.  Upon receipt by the Transfer Agent of evidence
reasonably satisfactory to it of the loss, theft, destruction or mutilation of
any Warrant Certificate, and, in case of loss, theft or destruction, of
indemnity or security reasonably satisfactory to it, and reimbursement to the
Company and/or the Transfer Agent of all reasonable expenses incidental thereto,
and upon surrender and cancellation of such Warrant Certificate, if mutilated,
the Transfer Agent will make and deliver a new Warrant Certificate of like
tenor, in lieu thereof.

          8.  Payment of Taxes.  The Company will pay all documentary stamp
              ----------------
taxes attributable to the initial issuance of the Warrants and of the Warrant
Shares upon the exercise of Warrants; provided, however, that the Company shall
not be required to pay any tax or taxes which may be payable in respect of any
transfer involved in the issuance of any Warrant Certificates or any
certificates for Warrant Shares in a name other than that of the registered
holder of such Warrant Certificate, and the Company shall not be required to
issue or deliver

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such Warrant Certificates unless or until the person or persons requesting the
issuance thereof shall have paid to the Company the amount of such tax or shall
have established to the satisfaction of the Company that such tax has been paid.

          9.  Statement on Warrants.  Irrespective of any adjustment in the
              ---------------------
number or kind of shares issuable upon the exercise of the Warrants or the
Exercise Price, Warrant Certificates theretofore or thereafter issued may
continue to express the same number and kind of shares and the same Exercise
Price as are stated in the Warrant Certificates  initially issuable pursuant to
this Agreement.

          10.  Registration.  The Company acknowledges that registered holders
               ------------
shall have the registration rights set forth in the Registration Rights
Agreement dated the date hereof between the Company and the Initial Holders.

          11.  Notices.
               -------

          All notices, requests, consents and other communications hereunder
shall be in writing and shall be deemed to have been duly made when delivered by
hand or sent by facsimile transmission (with receipt confirmed), or, if timely
delivered to an air courier guaranteeing overnight delivery service, on the next
business day, or five business days after being deposited in the mail, first
class, certified or registered, postage prepaid, return receipt requested, in
each case addressed as follows (or to such other place or places as either of
the parties shall designate by written notice to the other):

          (i)  if to registered holder, to the address set forth on the Warrant
               Register maintained by the Transfer Agent; and

          (ii) if to the Company, to:

                    Digex, Incorporated.
                    One Digex Plaza
                    Beltsville, Maryland 20705
                    Attention: Chief Financial Officer
                    Facsimile: (240) 264-2380

                    with a copy to:

                    Kronish Lieb Weiner & Hellman LLP
                    1114 Avenue of Americas
                    New York, NY 10036-7798
                    Attention: Ralph J. Sutcliffe, Esq.
                    Facsimile: (212) 479-6275

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<PAGE>

          12.  Amendment.  The Company with the consent of the registered
               ---------
holders of the unexercised Warrants evidencing at least a majority of the
Warrant Shares underlying the unexercised Warrants may amend or supplement this
Agreement or waive compliance by the Company in a particular instance with any
provision of this Agreement; provided that without the consent of each
registered holder affected, no such amendment shall (with respect to Warrants
held by a non-consenting registered holder) increase the Exercise Price or
decrease the number of Warrant Shares issuable upon exercise of any Warrant .

          13.  Successors.  Except as otherwise provided herein, all the
               ----------
covenants and provisions of this Agreement by or for the benefit of the Company
and the registered holders of the Warrants shall inure to the benefit of their
respective successors and assigns hereunder.

          14.  Governing Law.  This Agreement and each Warrant Certificate
               -------------
issued hereunder shall be deemed to be a contract made under the laws of the
State of Delaware and for all purposes shall be construed in accordance with the
laws of such State (without regard to the conflicts of law principles thereof).

          15.  Benefits of This Agreement.  Nothing in this Agreement shall be
               --------------------------
construed to give to any person other than the Company and the registered
holders of the unexercised Warrant Certificates any legal or equitable right,
remedy or claim under this Agreement; and this Agreement shall be for the sole
and exclusive benefit of the Company and such registered holders.  Prior to the
exercise of the Warrants, no holder of a Warrant Certificate, as such, shall be
entitled to any rights of a stockholder of the Company, including, without
limitation, the right to receive dividends or subscription rights, the right to
vote, to consent, to exercise any preemptive right, to receive any notice of
meetings of stockholders for the election of directors of the Company or any
other matter or to receive any notice of any proceedings of the Company, except
as may be specifically provided for herein.  The holders of the Warrants, as
such, are not entitled to share in the assets of the Company in the event of the
liquidation, dissolution or winding up of the Company's affairs.

          16.  Counterparts.  This Agreement may be executed in any number of
               ------------
counterparts and each of such counterparts shall for all purposes be deemed to
be an original, and such counterparts shall together constitute one and the same
instrument.

          17.  Headings.  The headings in this Agreement are intended solely for
               --------
convenience of reference and shall be given no effect in the construction or
interpretation of this Agreement.


                            [Signature Page Follows]

                                       11
<PAGE>

          IN WITNESS WHEREOF, the parties hereto have caused this Warrant
Agreement to be duly executed as of the day and year first above written.

                              DIGEX, INCORPORATED


                              By:  /s/ MARK K. SHULL
                                  ------------------
                                 Name: Mark K. Shull
                                 Title: Chief Executive Officer


                              MICROSOFT CORPORATION


                              By:  /s/  ROBERT J. HERBOLD
                                  ------------------------
                                 Name: Robert J. Herbold
                                 Title: Chief Operating Officer


                              CPQ HOLDINGS, INC.


                              By:  /s/  BEN K. WELLS
                                  ------------------------
                                 Name: Ben K. Wells
                                 Title: Vice President & Treasurer

                                       12
<PAGE>

                                   Exhibit A

Initial Holders                       Number of Warrants
---------------                       ------------------

Microsoft Corporation                 532,500

CPQ Holdings, Inc.                    532,500


                                      -i-
<PAGE>

                                   EXHIBIT B


                         [FORM OF WARRANT CERTIFICATE]


THE SECURITY (OR ITS PREDECESSOR) EVIDENCED HEREBY WAS ORIGINALLY ISSUED IN A
TRANSACTION EXEMPT FROM REGISTRATION UNDER SECTION 5 OF THE UNITED STATES
SECURITIES ACT OF 1933, AS AMENDED (THE "SECURITIES ACT").  THE SECURITY
EVIDENCED HEREBY MAY NOT BE OFFERED, SOLD OR OTHERWISE TRANSFERRED IN THE
ABSENCE OF SUCH REGISTRATION OR AN APPLICABLE EXEMPTION THEREFROM.

THE TRANSFER OF THE WARRANTS REPRESENTED BY THIS CERTIFICATE IS RESTRICTED IN
ACCORDANCE WITH THE WARRANT AGREEMENT REFERRED TO HEREIN.

                            EXERCISABLE ON OR BEFORE
                          5:00 P.M., NEW YORK TIME, on
                                January __, 2003

No. W-



                              WARRANT CERTIFICATE

          This Warrant Certificate certifies that, for value received,
_________________ having an address at ______________ ("Holder"), is the
registered holder of warrants (the "Warrants") to purchase, at any time and from
time to time after the date hereof until 5:00 P.M. New York time, on January
___, 2003, up to [               ] fully-paid and non-assessable shares (subject
to adjustment in certain events) of Class A Common Stock, par value $.01 per
share ("Common Stock"), of DIGEX, INCORPORATED, a Delaware corporation (the
"Company"), at the exercise price per share of $57.00, subject to adjustment in
certain events (the "Exercise Price"), upon surrender of this Warrant
Certificate, together with the attached Form of Election to Purchase duly
executed, and payment of the Exercise Price at the principal office of
Continental Stock Transfer & Trust Company (the "Transfer Agent"), but subject
to the terms and conditions set forth herein and in the Warrant Agreement dated
as of January ___, 2000 between the Company and the Initial Holders (the
"Warrant Agreement"). Payment of the

                                     -ii-
<PAGE>

Exercise Price shall not be made in cash. Each registered holder of the Warrants
shall exercise its rights to receive shares of Common Stock on a net basis, such
that without the exchange of any funds, such holder receives that number of
shares of Common Stock that would otherwise be issuable upon a cash exercise of
such Warrants less that number of shares of Common Stock having a current market
price (as defined in Section 3(b) of the Warrant Agreement) equal to the
aggregate cash Exercise Price that would otherwise have been paid by such holder
for the number of shares of Common Stock with respect to which such Warrant is
being exercised.

          This Warrant may be exercised at such times and in such amounts as are
provided for in the Warrant Agreement.  Each Warrant not exercised on or prior
to January ___,2003 shall become invalid and all rights hereunder, and all
rights in respect thereof under the Warrant Agreement, shall cease as of that
time.

          The Warrants evidenced by this Warrant Certificate are issued pursuant
to the Warrant Agreement, which Warrant Agreement is hereby incorporated by
reference in and made a part of this instrument and is hereby referred to for a
description of the rights, limitation of rights, obligations, duties and
immunities thereunder of the Company and the holders (the words "holders" or
"holder" meaning the registered holders or registered holder) of the Warrants.
A copy of the Warrant Agreement may be obtained by the holder(s) hereof upon
written request directed to the Company.

          The Warrant Agreement provides that upon the occurrence of certain
events, the Exercise Price and the type and/or number of the Company's
securities issuable upon exercise of the Warrants may, subject to certain
conditions, be adjusted.

          Upon due presentment for registration of transfer of this Warrant
Certificate at the principal office of the Transfer Agent, a new Warrant
Certificate or Warrant Certificates of like tenor and evidencing in the
aggregate a like number of Warrants shall be issued to the transferee(s) in
exchange for this Warrant Certificate, subject to the limitations provided
herein and in the Warrant Agreement, without any charge except for any tax or
other governmental charge imposed in connection therewith.


          Upon the exercise of less than all of the Warrants evidenced by this
Warrant Certificate, the Transfer Agent shall forthwith issue to the holder
hereof a new Warrant Certificate representing such number of unexercised
Warrants.

          The Company and the Transfer Agent may deem and treat the registered
holder(s) hereof as the absolute owner(s) of this Warrant Certificate
(notwithstanding any notation of ownership or other writing hereon made by
anyone), for the purpose of any exercise hereof and of any distribution to the
holder(s) hereof and for all other purposes, and neither the Company nor the
Transfer Agent shall be affected by any notice to the contrary.


                                     -iii-
<PAGE>

          All terms used in this Warrant Certificate which are not defined
herein and are defined in the Warrant Agreement shall have the meanings assigned
to them in the Warrant Agreement.


          IN WITNESS WHEREOF, the Company has caused this Warrant Certificate to
be duly executed under its corporate seal.

Dated: January ___, 2000

                              DIGEX, INCORPORATED


                              By:_____________________________
                                 Name:
                                 Title:

                                     -iv-
<PAGE>

                             [FORM OF ASSIGNMENT]



            (To be executed by the registered holder if such holder
                 desires to transfer the Warrant Certificate.)


          FOR VALUE RECEIVED, ________________________  hereby sells, assigns
and transfers unto ________________________________, whose address is
__________________________, this Warrant Certificate, together with all right,
title and interest therein, and does hereby irrevocably constitute and appoint
___________________________, Attorney to transfer the within Warrant Certificate
on the books of the within-named Company, with full power of substitution.

Dated:        Signature:____________________

                         (Signature must conform in all respects to name of
                         holder as specified on the face of the Warrant
                         Certificate.  Signature must be guaranteed by a bank or
                         trust company having an office or correspondent in the
                         United States or a broker or dealer which is a member
                         of a registered securities exchange or the National
                         Association of Securities Dealers, Inc.)


                         _________________________
                         (Insert Social Security or Other
                         Identifying Number of Holder)
<PAGE>

                        [FORM OF ELECTION TO PURCHASE]



          The undersigned hereby irrevocably elects to exercise the right,
represented by this Warrant Certificate, to purchase ________________ shares of
Common Stock , all in accordance with the terms of the Warrant Agreement, dated
January 12, 2000, by and among Digex, Incorporated and the initial holders of
the Warrants.

          The undersigned requests that a certificate for such shares of Common
Stock be registered in the name of _________________________________________,
whose address is _____________________________________________ and that such
certificate be delivered to _______________________________________ whose
address is _____________________________________________.


Dated:                   Signature:  ___________________

                         (Signature must conform in all respects to name of
                         holder as specified on the face of the Warrant
                         Certificate.  Signature must be guaranteed by a bank or
                         trust company having an office or correspondent in the
                         United States or a broker or dealer which is a member
                         of a registered securities exchange or the National
                         Association of Securities Dealers, Inc.)


                         _________________________
                         (Insert Social Security or Other
                         Identifying Number of Holder)