Document:

<PAGE>
                                                                    EXHIBIT 10.2

                               OPTION AGREEMENT

          OPTION AGREEMENT, dated as of June 5, 2000 (this "Agreement"), by and
between Data Critical Corporation, a Delaware corporation (the "Company"), and
Aether Systems, Inc., a Delaware corporation (the "Holder").

                                   RECITALS

          A.  The Company and the Holder are parties to that Common Stock
Purchase Agreement, dated as of June 2, 2000 (the "Purchase Agreement"),
pursuant to which the Holder purchased 1,230,770 shares of common stock, $0.001
par value per share, of the Company ("Common Stock"). This Agreement is the
Option Agreement discussed in the Purchase Agreement and certain
representations, warranties, covenants and agreements set forth in the Purchase
Agreement reference and are applicable to this Agreement.

          B.  The Company desires, upon the terms and subject to the conditions
set forth herein, to grant the Holder the right to purchase additional shares of
Common Stock.

          NOW, THEREFORE, in consideration of the foregoing and the agreements
set forth below, the parties agree as follows:

          1.  Grant of Option. The Company hereby grants to the Holder, on the
              ---------------
terms and subject to the conditions set forth herein, an option (the "Option")
to purchase for cash, in the manner set forth below, the aggregate number of
shares of Common Stock determined by dividing $10 million by the Per Share
Amount (such shares, the "Option Shares"); provided, however, that if the
acquisition by the Holder of the Option Shares would cause, as of the Closing of
any exercise of the Option, the Holder's ownership of Common Stock to exceed
19.9% of the issued and outstanding shares of capital stock of the Company,
calculated on the basis of the rules of the Nasdaq National Market relating to
required shareholder consent as in effect as of the date of the Closing, the
Option Shares shall be reduced to that number of shares of Common Stock
necessary to limit the Holder's total ownership to no more than 19.9% of the
issued and outstanding shares of capital stock of the Company, calculated on the
basis of the rules of the Nasdaq National Market relating to required
shareholder consent as in effect as of the date of the Closing. Subject to
Section 2(d) and adjustment as set forth in Section 7, the "Per Share Amount"
shall be equal to:

               a.  If the Exercise Notice (as defined herein) is delivered by
the Holder within 135 days of the date hereof (the "Initial Exercise Period"),
$15.00 per share; and

               b.  If the Exercise Notice is delivered by the Holder after 135
days of the date hereof, but before the Option Expiration Date (as defined
herein), $20.00 per share.

          2.  Exercise of Option; Closing and Deliveries.
              ------------------------------------------

               a.  In the event the Holder wishes to exercise the Option, the
Holder shall notify the Company that it intends to exercise the option (an
"Exercise Notice") and shall specify the applicable Per Share Amount as of the
date of such notice. The Exercise Notice shall also
<PAGE>

specify the place, date and time of the closing for the purchase of the Option
Shares (a "Closing"), which date shall be the first business day following the
satisfaction of all conditions to the Closing set forth in Section 5.

               b.   At the Closing, the Company shall deliver a certificate
registered in the name of the Holder or its assignee and representing the Option
Shares being purchased against payment of the Exercise Price by wire transfer of
immediately available funds to an account specified by the Company.

               c.   The Company shall not be required to issue fractions of
shares of Common Stock on the exercise of this Option. If any fraction of a
share of Common Stock would, except for the provisions of this Section 2(c), be
issuable upon the exercise of this Option, the Company shall purchase such
fraction for an amount in cash equal to the current value of such fraction,
computed in accordance with the determination of the Per Share Amount.

               d.   If the Purchaser delivers an Exercise Notice during the
Initial Exercise Period, but the Closing fails to occur during such Initial
Exercise Period, the Per Share Amount shall be $20.00 if the failure of the
Closing to take place during the Initial Exercise Period is due solely to the
failure of the Holder to satisfy the conditions set forth in Section 5(d) of
this Agreement.

     3.   Term of Option.  Except as may be necessary to comply with Section
          --------------
1, the Option may be exercised by the Holder in whole but not in part. Exercise
shall be by delivery of the Exercise Notice, at any time after the date hereof
and on or before 5:00 p.m., Eastern daylight time, on March 5, 2001 (the "Option
Expiration Date"), provided, however, that if such date is a day on which
                   --------- -------
banking institutions in the State of New York are authorized by law to close,
then the Option Expiration Date shall be the next succeeding day which shall not
be such a day.  The Option will terminate and be null and void if the Exercise
Notice is not delivered on or prior to the Option Expiration Date, provided,
                                                                   ---------
however, that if the Exercise Notice is delivered on or prior to the Option
-------
Expiration Date the Option will not be null and void merely because the related
Closing takes place following the Option Expiration Date unless the failure of
the Closing to take place prior to the Option Expiration Date is due solely to
the failure of the Holder to satisfy the conditions to Closing set forth in
Section 5(d) of this Agreement.  Termination of this Option shall neither
constitute a termination of the Purchase Agreement or any Other Transaction
Document (as defined in the Purchase Agreement) nor discharge, relieve or
release the Company or the Holder (a) for the consequences of (including
liability or claims for relief or remedies associated with) any breach,
violation or default by any such party to the Purchase Agreement or any Other
Transaction Document (including, without limitation, this Option) to the extent
occurring, arising or accruing prior to the Option Expiration Date or (b) from
performing, satisfying, or complying with, any and all of any such party's
agreements, covenants or conditions pursuant to the terms and conditions of the
Purchase Agreement or any Other Transaction Document.

     4.   Covenants.
          ---------

               a.   The Company will at all times reserve for issuance and/or
delivery upon exercise of this Option such number of shares of Common Stock as
shall be required for issuance

                                       2
<PAGE>

and delivery upon exercise of this Option. The Company will file with the Nasdaq
National Market a Notification Form for Listing of Additional Shares for an
amount of shares of Common Stock at least equal to the number of Option Shares
that may then be purchased.

               b.   If applicable, the parties will file as soon as practicable
following delivery of the Exercise Notice all filings that are required under
the Hart-Scott-Rodino Antitrust Improvements Act of 1976 ("HSR Act") relating to
the issuance of the Option Shares, respond as soon as practicable to all
inquiries received from the Federal Trade Commission or the Antitrust Division
of the Department of Justice for additional information or documentation,
respond in the most expeditions manner as practicable to all inquiries received
from any other government agency in connection with antitrust matters, and seek
early termination of any waiting period under the HSR Act.

               c.   The Company and the Holder shall use its best efforts to
cause all conditions precedent to the obligations of the Company and the Holder
to be satisfied. Upon the terms and conditions of this Agreement, the Company
and the Holder will use reasonable best efforts to take, or cause to be taken,
all action, and to do, or cause to be done, all things necessary, proper or
advisable consistent with Applicable Law (as defined in the Purchase Agreement)
to consummate the transactions contemplated herein and make effective in the
most expeditious manner practicable the issuance of the Option Shares in
accordance with the terms of this Agreement.

     5.   Conditions to Closing.  The obligation of the Company to issue the
          ---------------------
Option Shares to the Holder hereunder and of the Holder to purchase the Option
Shares from the Company hereunder is subject to the conditions that:

               a.   Any waiting periods under the HSR Act applicable to the
issuance of the Option Shares hereunder shall have expired or been terminated.

               b.   No injunction or order shall be in effect of any
Governmental Authority which restrains, enjoins or otherwise prohibits the
issuance of the Option Shares.

               c.   The Company, or counsel for the Company, shall have
delivered to the Holder such evidence as may reasonably be requested by the
Holder, which evidence may include an opinion of counsel, of the due
authorization and valid issuance of the Option Shares.

               d.   The representations and warranties of the Holder contained
in Section 2.1.4, Section 2.1.5 (except for the filing required under the HSR
Act in connection with the exercise of the Option), Section 2.1.6, Section
2.1.7, Section 2.1.8 and Section 2.1.9 of the Purchase Agreement shall be (i) in
the case of representations and warranties that are qualified as to materiality,
true and correct and (ii) in all other cases, true and correct in all material
respects, as of the Closing with the same force and effect as though made on and
as of the date of the Closing.

               e.   The representations and warranties of the Company contained
in Section 2.2 of the Purchase Agreement shall be (i) in the case of
representations and warranties that are qualified as to materiality, true and
correct and (ii) in all other cases, true and correct in all

                                       3
<PAGE>

material respect, as of the Closing with the same force and effect as though
made on and as of the date of the Closing.

For purposes of Section 5(d) and Section 5(e) of this Agreement only, all
references in the Purchase Agreement to the Purchase Agreement and Other
Transaction Documents shall be interpreted to refer only to this Agreement and
references in the Purchase Agreement to the Shares shall be interpreted to refer
only to the Option Shares.

     6.   No Impairment.  The Company shall not by any action including, without
          -------------
limitation, amending its certificate of incorporation or bylaws or through any
reorganization, transfer of assets, consolidation, merger, dissolution, issue or
sale of securities or any other voluntary action, avoid or seek to avoid the
observance or performance of any of the terms of this Agreement, but will at all
times in good faith assist in the carrying out of all such terms of this
Agreement and in the taking of all such actions as may be necessary or
appropriate to protect the rights of the Holder under this Agreement against
impairment.  Without limiting the generality of the foregoing, the Company will
(a) not, directly or indirectly, increase the par value of any shares of Common
Stock receivable upon the exercise of the Option above the amount payable
therefor upon such exercise immediately prior to such increase in par value, (b)
take all such action as may be necessary or appropriate in order that the
Company may validly and legally issue fully paid and nonassessable shares of
Common Stock upon the exercise of the Option and (c) use its commercially
reasonable best efforts to obtain all such authorizations, exemptions or
consents from any public regulatory body having jurisdiction thereof as may be
necessary to enable the Company to perform its obligations under this Option.

     7.   Adjustment of Purchase Price.  If at any time after the date hereof
          ----------------------------
the  number of shares of Common Stock outstanding (a) is increased by a stock
dividend payable in shares of Common Stock or by a subdivision or split of
shares of Common Stock or (b) is decreased by a combination of the outstanding
shares of Common Stock, then, following the record date for such action, the Per
Share Amount shall be appropriately decreased or increased, as the case may be,
in proportion to the relevant increase or decrease in outstanding shares.

     8.   Legends.  Upon issuance to the Holder of any Option Shares, such
          -------
Option Shares shall bear one or all of the following legends:

               a.   "THE SHARES REPRESENTED BY THIS CERTIFICATE HAVE NOT BEEN
               REGISTERED PURSUANT TO AN EFFECTIVE REGISTRATION STATEMENT UNDER
               THE SECURITIES ACT OF 1933, AS AMENDED, AND MAY NOT BE
               TRANSFERRED, SOLD, PLEDGED, HYPOTHECATED OR OTHERWISE DISPOSED OF
               UNLESS (i) (A) SUCH DISPOSITION IS PURSUANT TO AN EFFECTIVE
               REGISTRATION STATEMENT UNDER THE SECURITIES ACT OF 1933, AS
               AMENDED, (B) THE HOLDER HEREOF SHALL HAVE DELIVERED TO THE
               COMPANY EVIDENCE REASONABLY SATISFACTORY TO THE COMPANY, TO THE
               EFFECT THAT SUCH DISPOSITION IS EXEMPT FROM THE PROVISIONS OF
               SECTION 5 OF SUCH ACT OR (C) A NO-ACTION LETTER FROM THE
               SECURITIES AND EXCHANGE COMMISSION, REASONABLY SATISFACTORY TO
               COUNSEL FOR THE COMPANY, SHALL HAVE

                                       4
<PAGE>

               BEEN OBTAINED WITH RESPECT TO SUCH DISPOSITION AND (ii) SUCH
               DISPOSITION IS PURSUANT TO REGISTRATION UNDER ANY APPLICABLE
               STATE SECURITIES LAWS OR AN EXEMPTION THEREFROM."

               b.   Any legend required by the securities or "blue sky" laws of
any state to the extent such laws are applicable to the Option Shares
represented by the certificate so legended.

     9.   No Rights or Liabilities as Stockholder.  Nothing contained in this
          ---------------------------------------
Agreement shall be construed as conferring upon the Holder hereof, prior to the
exercise of the Option, any rights as a stockholder of the Company or as
imposing any liabilities on the Holder to purchase any securities or as a
stockholder of the Company, whether such liabilities are asserted by the Company
or by creditors or stockholders of the Company or otherwise. Without limiting
the foregoing, prior to the Closing hereunder the Holder shall have no right
with respect to the Option Shares to vote, consent, withhold consent or receive
any notices or otherwise have any rights as a stockholder with respect to such
Option Shares.

     10.  Lock-Up.  To the extent not inconsistent with applicable law, the
          -------
Holder hereby agrees that, during the period commencing on the date of the
Closing and ending one year from the date of the Closing, the Holder shall not,
without the consent of the Company sell or otherwise transfer or dispose of any
Option Shares.

     11.  Notices.  Except as otherwise provided, all notices which are
          -------
permitted or required under this Agreement shall be in writing and shall be
deemed given (a) when delivered personally, (b) if by fax upon transmission with
confirmation of receipt by the receiving party's facsimile terminal, (c) if sent
by documented overnight delivery service on the date delivered or (d) if sent by
mail, five (5) business days after being mailed by registered or certified mail,
return receipt postage prepaid, addressed as follows, or to such other person or
address as may be designated by notice to the other party:

     If to the Company, to:

     Data Critical Corporation
     19820 North Creek Parkway, Suite 100
     Bothell, Washington  98011
     Attn:  Michael E. Singer
     Phone:  (425) 482-7025
     Facsimile:  (425) 482-7010

     with a copy (which shall not constitute notice) to:

     Orrick, Herrington & Sutcliffe LLP
     701 Fifth Avenue, Suite 6500
     Seattle, Washington 98104
     Attn: Scott J. Moore
     Phone:  (206) 839-4300
     Facsimile: (206) 839-4301

                                       5
<PAGE>

     If to the Purchaser, to:

     Aether Systems, Inc.
     11460 Cronridge Drive
     Owings Mills, Maryland  21117
     Attn:  Brian W. Keane
     Phone:  (410) 654-6400
     Facsimile: (410) 654-6554

     with a copy (which shall not constitute notice) to:

     Jones, Day, Reavis & Pogue
     901 Lakeside Ave.
     Cleveland, Ohio  44114
     Attn: Christopher M. Kelly
     Phone:  (216) 586-3939
     Facsimile:  (216) 579-0212

     12. Fees and Expenses.  The parties will share equally the filing fees
         -----------------
related to any filing required under the HSR Act.  At any Closing, the Company
will pay all expenses that may be payable in connection with the preparation,
issuance and delivery of the certificates representing the Option Shares under
this Agreement.  All other expenses incurred in connection with the negotiation,
preparation, execution and performance of this Agreement shall be paid by the
party incurring such expenses.

     13. Assignment.  This Agreement will be binding upon the parties hereto and
         ----------
will inure to the benefit of the parties hereto and their legal successors and
permitted assigns.  This Agreement and the transactions contemplated hereby may
not be assigned or otherwise transferred, in whole or in part, by operation of
law or otherwise, without the prior written consent of the other party.

     14. Counterparts.  This Agreement may be executed in two or more
         ------------
counterparts, each of which when so executed and delivered, shall be an original
instrument, but such counterparts together shall constitute a single agreement.

     15. Governing Law.  THIS AGREEMENT AND THE RIGHTS AND OBLIGATIONS OF THE
         -------------
PARTIES HEREUNDER SHALL BE GOVERNED BY THE SUBSTANTIVE LAWS OF THE STATE OF NEW
YORK APPLICABLE TO CONTRACTS MADE AND TO BE PERFORMED THEREIN, WITHOUT GIVING
EFFECT TO THE CONFLICTS OF LAWS RULES THEREOF.

     16. Headings.  The headings contained in this Agreement are for reference
         --------
purposes only and shall not affect the meaning or interpretation of this
Agreement.

     17. Severability.  Any provision of this Agreement which is invalid or
         ------------
unenforceable shall be ineffective to the extent of such invalidity or
unenforceability, provided that such

                                       6
<PAGE>

invalidity or unenforceability does not deny any party the material benefits of
the transactions for which it has bargained, such invalidity or unenforceability
shall not affect in any way the remaining provisions hereof.

     18.  Modification and Amendment.  This Agreement may not be modified or
          --------------------------
amended except by written agreement specifically referring to this Agreement and
signed by the parties hereto.

     19.  Waiver.  No waiver of a breach or default hereunder shall be
          ------
considered valid unless in writing and signed by the party giving such waiver,
and no such waiver shall be deemed a waiver of any subsequent breach or default
of the same or similar nature.

     20.  Terms.  Capitalized terms used herein but not defined shall have the
          -----
meanings set forth in the Purchase Agreement.

                           [Signature Page Follows]

                                       7
<PAGE>

     IN WITNESS WHEREOF, this Agreement has been duly executed and delivered by
the parties hereto on the day and year first written above.

                                   DATA CRITICAL CORPORATION

                                   By: /s/ Jeffrey S. Brown
                                       --------------------------
                                       Name:  Jeffrey S. Brown
                                              -------------------
                                       Title: President/CEO
                                              -------------------

                                   AETHER SYSTEMS, INC.

                                   By: /s/ Brian W. Keane
                                       --------------------------
                                      Name: Brian W. Keane
                                            ---------------------
                                      Title: SVP
                                             --------------------<PAGE>

                                                                   EXHIBIT 10.13
February 17, 1999

Mr. Joe Caffarelli
2919 216th Avenue NE
Redmond, WA 98053

Dear Joe:

     This letter confirms that your employment with Airspan Communications
Corporation.  You will be working as Senior Vice President and Chief Financial
Officer, reporting to me.  The effective start date will be April 1, 1999.

     Compensation will be composed of several elements:

        .  Base Salary:  $200,000 per year, paid twice a month
        .  Annual Bonus:  % function bonus based on Gross Profits/kicks in at
           $50,000 for $13.12M gross profit for 1999.
        .  Stock options totaling 343,000 shares vesting monthly over 4 years
           with a 12-month initial period where no shares vest. These options
           are subject to board approval and will be granted 18 cents a share or
           alternatively at latest closing round (17.5 cents)

     An additional adjustment will be paid of $50,000 less approximate taxes per
12-month period to cover all cost of living and income tax liabilities arising
due to your residency in the UK.  This compensation will only be paid while you
are resident in the UK.

     You will receive a signing bonus of $30,000 at the end of April.  In the
event that you resign from Airspan within twelve months, this bonus will be
refunded to the company.

     Four weeks of annual vacation will be provided per year.

     The cost of shipping for a small container of personal goods will be re-
inbursed by our company with a rental management fee for your Seattle home with
a maximum monthly amount of $500, payable on presentation of expenses.  Should
you elect to transport your dog to the UK, reasonable quarantine and transport
costs will be re-imbursed.  Furthermore, the company will cover the rental of a
small storage container in the Seattle area with a monthly limit of $200 for the
period while you are working in the UK.  If desired you can combine the total of
$200 rental and $500 management fee in an alternative way provided the total
does not exceed $700.

     Assuming continued employment should it be necessary to locate in the US,
moving expenses back to Airspan within the US will also be reimbursed.

     In the unlikely event of a termination of employment initiated by the
company, we will provide a severance payment of 6 months basic salary and an
allowance to relocate back to Seattle consistent with the reimbursed expenses
for the move to the UK.
<PAGE>

     You will be responsible for all applicable UK taxes as well as US taxes on
your compensation.  The services of Ernst and Young or associated auditor will
be available to assist you within reason for the initial years' filing of UK
taxes.

     This offer is contingent on a satisfactory medical evaluation and the forms
for this simple evaluation will be forwarded to you shortly.  I request that you
can complete these forms prior to your starting date.

     Joe, on behalf of the Airspan Communications Corporation, I look forward to
your membership on our team and look forward to seeing you soon.

Sincerely,

/s/ Eric Stonestrom

Eric Stonestrom
President and Chief Executive Officer

                                      -2-
<PAGE>

ADDENDUM TO J CAFFARELLI OFFER LETTER
RELOCATION AGREEMENT:  US TO UK

ADMINISTRATION OF THE RELOCATION AGREEMENT

1.   PURPOSE

This agreement is designed to provide financial assistance and advisory support
for Airspan employees relocating to the UK to take up employment with the
Company.

2.   EXPENSES COVERED BY THIS AGREEMENT

Outlined in this agreement are the relocation expenses which the Company is
prepared to reimburse to you (if not already covered by your offer letter) and,
where possible, maximum expenditure is indicated.  Where it is not indicated the
Company expects reasonable expenditure to be submitted.  If you are in any doubt
as to what the Company deems reasonable, please contact the HR Department with
written estimates prior to expenditure for approval.  Items not included in this
agreement will not be reimbursed except those referred to in paragraph 6 of this
policy.

3.   ADMINISTRATION

This agreement will be administered by the Human Resources Department in the UK.

4.   ELIGIBILITY

You will only be eligible for relocation reimbursement whilst in employment with
the Company.  You will not be eligible for relocation reimbursement during any
notice period if you resign from the Company nor if your employment is
terminated for cause.

5.   RECORD KEEPING

The tax implications involved with relocation require very careful record
keeping by both you and the Company.  For all expenses you must submit
relocation expenses reports in a timely manner with original receipts, to the
Human Resources Department for processing.  The reimbursed ceiling imposed by
the Inland Revenue in the UK for relocation expenses before they become taxable
benefit is (Pounds)8,000.  You are therefore requested to establish mutually
agreed monthly communication with the HR Department to monitor relocation
expenditure.

6.   EXPENSES NOT COVERED BY THIS AGREEMENT

The Company recognises that special circumstances and contingencies may occur in
a relocation.  No one plan such as this can cover every conceivable situation.
If you encounter an unusual problem or a circumstance which does not seem to be
adequately covered in this policy, the Human Resources Department will make
every effort to provide you with the answers and assistance needed.  All
agreement deviations require the approval of the President and CEO.

                                      -3-
<PAGE>

7.   CAR RENTAL

If you do not have access to your car when you arrive in the UK, the Company
will reimburse you for rental for one car for 90 days from your date of entry to
the UK, to be arranged through the Company.  It is your responsibility to ensure
you hold a valid and current driving license to drive in the UK.  At the end of
the 90-day period you can either pay the company on a monthly invoice basis for
the use of the car until the end of its lease or return the car to the company
and make your own arrangements.

8.   TEMPORARY LIVING EXPENSES

The Company will pay for temporary accommodation in the UK in accommodation to
be arranged through the Company for a maximum period of 90 days.  All expenses
must be submitted through the Company's expenses procedure and must be
authorised by the President and CEO (as your line manager).

9.   MOVING EXPENSES

The following goods will not be moved, stored, handled or insured at the
Company's expense:

   .  Motorcycles
   .  Recreational Motor Vehicles or Airplanes
   .  Boats (too big for regular shipment along with household goods)
   .  Patio slate
   .  Planes or gliders
   .  Fertiliser
   .  Cement
   .  Frozen foods
   .  Shrubbery
   .  Firewood
   .  Lumber or other building material
   .  Sand
   .  Animals larger than a dog or a cat
   .  Portable swimming pools/hot tubs
   .  Live plans

In addition, the Company will not pay car storage costs.  The Company is not
responsible for the value of any special collections you ship, including
jewellery or antique furniture.  It is recommended, therefore, that you store or
hand carry these items to protect them, or arrange for special insurance at your
own expense.

You must pay special handling or additional shipping cost for these items:

   .  Pianos or other large objects;

                                      -4-
<PAGE>

   .  Hobby or shop equipment
   .  Plants and shrubs; and
   .  Other similar personal items.

10.  REPAYMENT OF RELOCATION EXPENSES

Should you resign your position with the Company within one year from 1st April
1999 you hereby undertake to repay the Company on a pro-rata basis (11/12ths in
month 1 to 1/12th in month 12) the total relocation expenditure reimbursed to
your or paid on your behalf.  Repayment may take the form of payroll deduction
expense claim offset or personal cheque.

Signed /s/ Joe Caffarelli                   Date   April 30, 1999
      --------------------------                ------------------
      Joe Caffarelli

                                      -5-

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