<PAGE>   1
                                                                    EXHIBIT 4.19


NEITHER THIS WARRANT NOR THE SECURITIES INTO WHICH THIS WARRANT IS EXERCISABLE
HAVE BEEN REGISTERED WITH THE SECURITIES AND EXCHANGE COMMISSION OR THE
SECURITIES COMMISSION OF ANY STATE IN RELIANCE UPON AN EXEMPTION FROM
REGISTRATION UNDER SECURITIES ACT OF 1933, AS AMENDED (THE "SECURITIES ACT"),
AND, ACCORDINGLY, MAY NOT BE OFFERED OR SOLD EXCEPT PURSUANT TO AN EFFECTIVE
REGISTRATION STATEMENT UNDER THE SECURITIES ACT OR PURSUANT TO AN AVAILABLE
EXEMPTION FROM THE REGISTRATION REQUIREMENTS THEREUNDER AND IN COMPLIANCE WITH
APPLICABLE STATE SECURITIES OR BLUE SKY LAWS.


                       ILLINOIS SUPERCONDUCTOR CORPORATION

                                     WARRANT
                                     -------

Warrant No. WCN-00_                                         Dated March 31, 1999

         Illinois Superconductor Corporation, a Delaware corporation (the
"Company"), hereby certifies that, for value received,
__________________________, or its registered assigns (the "Holder"), is
entitled, subject to the terms set forth below, to purchase from the Company up
to a total of _______ shares of Common Stock, $.001 par value per share (the
"Common Stock"), of the Company (each such share, a "Warrant Share" and all such
shares, the "Warrant Shares") at an exercise price equal to $1.4625 per share
(as adjusted from time to time as provided in Section 8, the "Exercise Price"),
at any time and from time to time from the date hereof through and including
March 31, 2002 (the "Expiration Date"), and subject to the following terms and
conditions:

         1. Registration of Warrant. The Company shall register this Warrant,
upon records to be maintained by the Company for that purpose (the "Warrant
Register"), in the name of the record Holder hereof from time to time. The
Company may deem and treat the registered Holder of this Warrant as the absolute
owner hereof for the purpose of any exercise hereof or any distribution to the
Holder, and for all other purposes, and the Company shall not be affected by
notice to the contrary.

         2. Registration of Transfers and Exchanges.

         (a) The Company shall register the transfer of any portion of this
Warrant in the Warrant Register, upon surrender of this Warrant, with the Form
of Assignment attached hereto duly completed and signed and a written opinion of
Holder's counsel that such transfer is exempt from registration under the
Securities Act, to the Company at the office specified in or

<PAGE>   2
pursuant to Section 3(b); provided, however that the Holder shall not make any
transfers to any transferee pursuant to this Section for the right to acquire
less than 1,000 Warrant Shares. Upon any such registration or transfer, a new
warrant to purchase Common Stock, in substantially the form of this Warrant (any
such new warrant, a "New Warrant"), evidencing the portion of this Warrant so
transferred shall be issued to the transferee and a New Warrant evidencing the
remaining portion of this Warrant not so transferred, if any, shall be issued to
the transferring Holder. The acceptance of the New Warrant by the transferee
thereof shall be deemed the acceptance of such transferee of all of the rights
and obligations of a holder of a Warrant. If this Warrant is duly assigned in
accordance with the terms hereof, then the Company agrees, upon the request of
the assignee, to amend or supplement promptly any effective registration
statement covering the Warrant Shares so that the direct assignee of the
original Holder is added as a selling stockholder thereunder.

         (b) This Warrant is exchangeable, upon the surrender hereof by the
Holder to the office of the Company specified in or pursuant to Section 3(b) for
one or more New Warrants in the name of such Holder, evidencing in the aggregate
the right to purchase the number of Warrant Shares which may then be purchased
hereunder. Any such New Warrant will be dated the date of such exchange.

         3. Duration and Exercise of Warrants.

         (a) This Warrant shall be exercisable by the registered Holder on any
business day before 5:30 P.M., New York time, at any time and from time to time
up to and including the Expiration Date. At 5:30 P.M., New York time on the
Expiration Date, the portion of this Warrant not exercised prior thereto shall
be and become void and of no value.

         (b) Upon surrender of this Warrant, with the Form of Election to
Purchase attached hereto duly completed and signed, to the Company at its office
at 451 Kingston Court, Mt. Prospect, Illinois 60056, Attention: General Counsel,
or at such other address as the Company may specify in writing to the then
registered Holder, and upon payment of the Exercise Price multiplied by the
number of Warrant Shares that the Holder intends to purchase hereunder, in
lawful money of the United States of America, in cash or by certified or
official bank check or checks or wire transfer of immediately available funds,
all as specified by the Holder in the Form of Election to Purchase, the Company
shall promptly (but in no event later than three (3) trading days after the Date
of Exercise (as defined herein)) issue or cause to be issued and cause to be
delivered to or upon the written order of the Holder and in such name or names
as the Holder may designate, a certificate for the Warrant Shares issuable upon
such exercise, free of restrictive legends other than as required by the
Securities Purchase Agreement, dated as of March 31, 1999, between the Company
and the Purchasers listed therein, including the initial Holder of this Warrant
(the "Purchase Agreement"). Any person so designated by the Holder to receive
Warrant Shares shall be deemed to have become holder of record of such Warrant
Shares as of the Date of Exercise of this Warrant.

         A "Date of Exercise" means the date on which the Company shall have
received (i) this Warrant (or any New Warrant, as applicable), with the Form of
Election to Purchase attached hereto (or attached to such New Warrant)
appropriately completed and duly signed, and (ii)





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<PAGE>   3
payment of the Exercise Price for the number of Warrant Shares so indicated by
the Holder hereof to be purchased.

         (c) This Warrant shall be exercisable, either in its entirety or, from
time to time, for a portion of the number of Warrant Shares so long as at least
1,000 Warrant Shares are purchased in any one exercise, unless such exercise
would result in the Holder holding less than 1,000 Warrant Shares. If less than
all of the Warrant Shares which may be purchased under this Warrant are
exercised at any time, the Company shall issue or cause to be issued to the
Holder, at its expense, a New Warrant evidencing the right to purchase the
remaining number of Warrant Shares for which no exercise has been evidenced by
this Warrant.

         (d) If and while the Warrant Shares issuable upon the exercise of this
Warrant are not registered for public resale pursuant to an effective
registration statement with a current available prospectus, then upon exercise
of this Warrant the aggregate Exercise Price may be paid by the Holder notifying
the Company that it should subtract from the number of Warrant Shares issuable
to the Holder upon such exercise an amount of Warrant Shares, the aggregate Per
Share Market Value (as defined in the Purchase Agreement) of which, as
determined on the date immediately preceding the date of the Form of Election to
Purchase, equals such aggregate Exercise Price of the Warrant Shares for which
this Warrant is being exercised.

         (e) Notwithstanding anything to the contrary herein, the Holder may not
use its ability to exercise this Warrant if such exercise would result in the
total number of shares of Common Stock deemed beneficially owned by the Holder
(other than by virtue of the ownership of this Warrant or ownership of other
securities that have limitations on a holder's right to convert or exercise
similar to those limitations set forth herein), together with all shares of
Common Stock deemed beneficially owned by the Holder's Affiliates (as defined in
the Purchase Agreement) that would be aggregated for purposes of determining a
group under Section 13(d) of the Exchange Act, exceeding 9.9% of the total
issued and outstanding shares of the Company's Common Stock (the "Restricted
Ownership Percentage"); provided that (w) the Holder shall have the right, at
any time and from time to time, to reduce the Restricted Ownership Percentage
applicable to it immediately upon written notice to the Company, (x) the Holder
shall have the right to increase its Restricted Ownership Percentage and
otherwise waive in whole or in part the restrictions of this Section 3(e)
immediately upon written notice to the Company in the event of an occurrence or
notice of an intended or pending Change of Control (as defined in the Purchase
Agreement)(a "Change of Control Notice") or the delivery by the Company of a
notice of a redemption of the Company's 6% Convertible Notes or the Company's 2%
Senior Convertible Notes by the Company (a "Redemption Notice") and, (y) the
Holder can make subsequent adjustments pursuant to (w) or (x) any number of
times (which adjustment shall be effective immediately). The delivery of an
exercise notice by the Holder shall be deemed a representation by the Holder
that it is in compliance with this paragraph.

         4. [INTENTIONALLY OMITTED]

         5. Payment of Taxes. The Company will pay all documentary stamp taxes
attributable to the issuance of Warrant Shares upon the exercise of this
Warrant; provided,




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<PAGE>   4

however, that the Company shall not be required to pay any tax which may be
payable in respect of any transfer involved in the registration of any
certificates for Warrant Shares or Warrants in a name other than that of the
Holder, and the Company shall not be required to issue or cause to be issued or
deliver or cause to be delivered the certificates for Warrant Shares 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. The Holder shall be responsible for
all other tax liability that may arise as a result of holding or transferring
this Warrant or receiving Warrant Shares upon exercise hereof.

         6. Replacement of Warrant. If this Warrant is mutilated, lost, stolen
or destroyed, the Company may in its discretion issue or cause to be issued in
exchange and substitution for and upon cancellation hereof, or in lieu of and
substitution for this Warrant, a New Warrant, but only upon receipt of evidence
reasonably satisfactory to the Company of such loss, theft or destruction and
indemnity. Applicants for a New Warrant under such circumstances shall also
comply with such other reasonable regulations and procedures and pay such other
reasonable charges as the Company may prescribe.

         7. Reservation of Warrant Shares. The Company covenants that it shall
comply with the provisions of Section 3.13 of the Purchase Agreement. Subject to
Section 3.13 of the Purchase Agreement, the Company covenants that, following
its June 9, 1999 stockholder meeting, it will at all times reserve and keep
available out of the aggregate of its authorized but unissued Common Stock,
solely for the purpose of enabling it to issue Warrant Shares upon exercise of
this Warrant as herein provided, the number of Warrant Shares which are then
issuable and deliverable upon the exercise of this entire Warrant, free from
preemptive rights or any other actual contingent purchase rights of persons
other than the Holders (taking into account the adjustments and restrictions of
Section 8). The Company covenants that all Warrant Shares that shall be so
issuable and deliverable shall, upon issuance and the payment of the applicable
Exercise Price in accordance with the terms hereof, be duly authorized, validly
issued, fully paid and nonassessable.

         8. Certain Adjustments. The Exercise Price and number of Warrant Shares
issuable upon exercise of this Warrant are subject to adjustment from time to
time as set forth in this Section 8. Upon each such adjustment of the Exercise
Price pursuant to this Section 8, the Holder shall thereafter prior to the
Expiration Date be entitled to purchase, at the Exercise Price resulting from
such adjustment, the number of Warrant Shares obtained by multiplying the
Exercise Price in effect immediately prior to such adjustment by the number of
Warrant Shares issuable upon exercise of this Warrant immediately prior to such
adjustment and dividing the product thereof by the Exercise Price resulting from
such adjustment.

         (a) If the Company, at any time while this Warrant is outstanding, (i)
shall pay a stock dividend (except scheduled dividends paid on outstanding
preferred stock as of the date hereof which contain a stated divided rate) or
otherwise make a distribution or distributions on shares of its Common Stock (as
defined below) (or on any other class of capital stock and not the Common Stock)
payable in shares of Common Stock, (ii) subdivide outstanding shares of Common
Stock into a larger number of shares, or (iii) combine outstanding shares of
Common



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<PAGE>   5
Stock into a smaller number of shares, the Exercise Price shall be
multiplied by a fraction of which the numerator shall be the number of shares of
Common Stock (excluding treasury shares, if any) outstanding before such event
and of which the denominator shall be the number of shares of Common Stock
(excluding treasury shares, if any) outstanding after such event. Any adjustment
made pursuant to this Section shall become effective immediately after the
record date for the determination of stockholders entitled to receive such
dividend or distribution and shall become effective immediately after the
effective date in the case of a subdivision or combination, and shall apply to
successive subdivisions and combinations.

         (b) In case of any reclassification of the Common Stock, any
consolidation or merger of the Company with or into another person, the sale or
transfer of all or substantially all of the assets of the Company or any
compulsory share exchange pursuant to which the Common Stock is converted into
other securities, cash or property, then the Holder shall have the right
thereafter to exercise this Warrant only into the shares of stock and other
securities and property receivable upon or deemed to be held by holders of
Common Stock following such reclassification, consolidation, merger, sale,
transfer or share exchange, and the Holder shall be entitled upon such event to
receive such amount of securities or property equal to the amount of Warrant
Shares such Holder would have been entitled to had such Holder exercised this
Warrant immediately prior to such reclassification, consolidation, merger, sale,
transfer or share exchange, subject to such further adjustments as set forth in
this Section 8. The terms of any such consolidation, merger, sale, transfer or
share exchange shall include such terms so as to continue to give to the Holder
the right to receive the securities or property set forth in this Section 8(b)
upon any exercise following any such reclassification, consolidation, merger,
sale, transfer or share exchange.

         (c) If the Company, at any time while this Warrant is outstanding,
shall distribute to all holders of Common Stock evidences of its indebtedness or
assets or rights or warrants to subscribe for or purchase any security
(excluding those referred to in Section 8(a) and (b)), then in each such case
the Exercise Price shall be determined by multiplying the Exercise Price in
effect immediately prior to the record date fixed for determination of
stockholders entitled to receive such distribution by a fraction of which the
denominator shall be the Exercise Price determined as of the record date
mentioned above, and of which the numerator shall be such Exercise Price on such
record date less the then fair market value at such record date of the portion
of such assets or evidence of indebtedness so distributed applicable to one
outstanding share of Common Stock as determined by the Board of Directors of the
Company acting in good faith.

         (d) For the purposes of this Section 8, the following clauses shall
also be applicable:

                  (i) Record Date. In case the Company shall take a record of
         the holders of its Common Stock for the purpose of entitling them (A)
         to receive a dividend or other distribution payable in Common Stock or
         in securities convertible or exchangeable into shares of Common Stock,
         or (B) to subscribe for or purchase Common Stock or securities
         convertible or exchangeable into shares





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<PAGE>   6
                                      


         of Common Stock, then such record date shall be deemed to be the date
         of the issue or sale of the shares of Common Stock deemed to have been
         issued or sold upon the declaration of such dividend or the making of
         such other distribution or the date of the granting of such right of
         subscription or purchase, as the case may be.

                  (ii) Treasury Shares. The number of shares of Common Stock
         outstanding at any given time shall not include shares owned or held by
         or for the account of the Company, and the disposition of any such
         shares shall be considered an issue or sale of Common Stock.

         (e) All calculations under this Section 8 shall be made to the nearest
cent or the nearest 1/100th of a share, as the case may be.

         (f) Whenever the Exercise Price is adjusted pursuant to Section 8(c)
above, the Holders of Warrants representing a majority in interest of the
Warrant Shares, after receipt of the determination by the Company's Board of
Directors (the "Board"), shall have the right to select an appraiser at the
Holder's cost and expense (which shall be a nationally recognized accounting
firm), in which case the adjustment shall be equal to the average of the
adjustments recommended by each of the Board and such appraiser. The Holders
shall promptly mail or cause to be mailed to the Company, a notice setting forth
the Exercise Price after such adjustment and setting forth a brief statement of
the facts requiring such adjustment. Such adjustment shall become effective
immediately after the record date mentioned above.

         (g) If:

                  (i) the Company shall declare a dividend (or any other
         distribution) on its Common Stock; or

                  (ii) the Company shall declare a special nonrecurring cash
         dividend on or a redemption of its Common Stock; or

                  (iii) the Company shall authorize the granting to all holders
         of the Common Stock rights or warrants to subscribe for or purchase any
         shares of capital stock of any class or of any rights; or

                  (iv) the approval of any stockholders of the Company shall be
         required in connection with any reclassification of the Common Stock of
         the Company, any consolidation or merger to which the Company is a
         party, any sale or transfer of all or substantially all of the assets
         of the Company, or any compulsory share exchange whereby the Common
         Stock is converted into other securities, cash or property; or

                  (v) the Company shall authorize the voluntary dissolution,
         liquidation or winding up of the affairs of the Company,



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<PAGE>   7

         then the Company shall cause to be mailed to each Holder at their last
addresses as they shall appear upon the Warrant Register, at least 30 calendar
days prior to the applicable record or effective date hereinafter specified, a
notice stating (x) the date on which a record is to be taken for the purpose of
such dividend, distribution, redemption, rights or warrants, or if a record is
not to be taken, the date as of which the holders of Common Stock of record to
be entitled to such dividend, distributions, redemption, rights or warrants are
to be determined or (y) the date on which such reclassification, consolidation,
merger, sale, transfer or share exchange is expected to become effective or
close, and the date as of which it is expected that holders of Common Stock of
record shall be entitled to exchange their shares of Common Stock for
securities, cash or other property deliverable upon such reclassification,
consolidation, merger, sale, transfer, share exchange, dissolution, liquidation
or winding up; provided, however, that the failure to mail such notice or any
defect therein or in the mailing thereof shall not affect the validity of the
corporate action required to be specified in such notice.

         9. Fractional Shares. The Company shall not be required to issue or
cause to be issued fractional Warrant Shares on the exercise of this Warrant.
The number of full Warrant Shares which shall be issuable upon the exercise of
this Warrant shall be computed on the basis of the aggregate number of Warrant
Shares purchasable on exercise of this Warrant so presented. If any fraction of
a Warrant Share would, except for the provisions of this Section 9, be issuable
on the exercise of this Warrant, the Company shall, at its option, (i) pay an
amount in cash equal to the Exercise Price multiplied by such fraction or (ii)
round the number of Warrant Shares issuable, up to the next whole number.

         10. Notices. Any and all notices or other communications or deliveries
hereunder shall be in writing and shall be deemed to have been delivered (i)
upon receipt, when delivered personally; (ii) when sent by facsimile, upon
receipt if received on a Business Day prior to 5:00 p.m. (Central Time), or the
first Business Day following such receipt if received on a Business Day after
5:00 p.m. (Central Time); or (iii) upon receipt, when deposited with a
nationally recognized overnight express courier service, fully prepaid, in each
case properly addressed to the party to receive the same. The addresses and
facsimile number for such communications shall be: (1) if to the Company, to
Illinois Superconductor Corporation, 451 Kingston Court, Mt. Prospect, Illinois
60056, Attention: General Counsel, or to facsimile no. (847) 391-5015, or (ii)
if to the Holder, to the Holder at the address or facsimile number appearing on
the Warrant Register or such other address or facsimile number as the Holder may
provide to the Company in accordance with this Section 10.

         11. Warrant Agent.

         (a) The Company shall serve as warrant agent under this Warrant. Upon
thirty (30) days' notice to the Holder, the Company may appoint a new warrant
agent. 

         (b) Any corporation into which the Company or any new warrant agent may
be merged or any corporation resulting from any consolidation to which the
Company or any new warrant agent shall be a party or any corporation to which
the Company or any new warrant agent transfers substantially all of its
corporate trust or shareholders services business shall be a successor warrant
agent under this Warrant without any further act. Any such 




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<PAGE>   8

successor warrant agent shall promptly cause notice of its succession as warrant
agent to be mailed (by first class mail, postage prepaid) to the Holder at the
Holder's last address as shown on the Warrant Register.

         12. Miscellaneous.

         (a) This Warrant shall be binding on and inure to the benefit of the
parties hereto and their respective successors and permitted assigns. This
Warrant may be amended only in writing signed by the Company and the Holder.

         (b) Subject to Section 12(a), above, nothing in this Warrant shall be
construed to give to any person or corporation other than the Company and the
Holder any legal or equitable right, remedy or cause under this Warrant; this
Warrant shall be for the sole and exclusive benefit of the Company and the
Holder.

         (c) This Warrant shall be governed by and construed and enforced in
accordance with the internal laws of the State of New York without regard to the
principles of conflicts of law thereof.

         (d) The headings herein are for convenience only, do not constitute a
part of this Warrant and shall not be deemed to limit or affect any of the
provisions hereof.

         (e) In case any one or more of the provisions of this Warrant shall be
invalid or unenforceable in any respect, the validity and enforceability of the
remaining terms and provisions of this Warrant shall not in any way be affected
or impaired thereby and the parties will attempt in good faith to agree upon a
valid and enforceable provision which shall be a commercially reasonable
substitute therefor, and upon so agreeing, shall incorporate such substitute
provision in this Warrant.




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<PAGE>   9

         IN WITNESS WHEREOF, the Company has caused this Warrant to be duly
executed by its authorized officer as of the date first indicated above.


                                      ILLINOIS SUPERCONDUCTOR CORPORATION       
                
                
                
                                      By:  /s/    Edward W. Laves
                                          --------------------------------------
                                          Name:   Edward W. Laves
                                          Title:  President


<PAGE>   10


                          FORM OF ELECTION TO PURCHASE

(To be executed by the Holder to exercise the right to purchase shares of Common
Stock under the foregoing Warrant)

To Illinois Superconductor Corporation:

         In accordance with the Warrant enclosed with this Form of Election to
Purchase, the undersigned hereby irrevocably elects to purchase _____________
shares of Common Stock ("Common Stock"), $.001 par value per share, of Illinois
Superconductor Corporation (the "Company") and encloses herewith $________ in
cash or certified or official bank check or checks or by wire transfer of
immediately available funds or (to the extent permitted by the terms of the
Warrant) hereby notifies the Company to effect a "cashless" exercise by
subtracting ___________ shares of Common Stock valued at $________ per share
from the shares of Common Stock issuable hereby, which sum represents the
aggregate Exercise Price (as defined in the Warrant) for the number of shares of
Common Stock to which this Form of Election to Purchase relates, together with
any applicable taxes payable by the undersigned pursuant to the Warrant. The
undersigned represents that the number of shares of Common Stock issuable
pursuant to this Form of Election to Purchase does not violate or breach the
restrictions on exercise contained in Section 3(e) of the Warrant.

         The undersigned requests that certificates for the shares of Common
Stock issuable upon this exercise be issued in the name of

                                               PLEASE INSERT SOCIAL SECURITY OR
                                               TAX IDENTIFICATION NUMBER

                                               --------------------------------

--------------------------------------------------------------------------------
                         (Please print name and address)


--------------------------------------------------------------------------------

--------------------------------------------------------------------------------

         If the number of shares of Common Stock issuable upon this exercise
shall not be all of the shares of Common Stock which the undersigned is entitled
to purchase in accordance with the enclosed Warrant, the undersigned requests
that a New Warrant (as defined in the Warrant) evidencing the right to purchase
the shares of Common Stock not issuable pursuant to the exercise evidenced
hereby be issued in the name of and delivered to:


--------------------------------------------------------------------------------
                         (Please print name and address)

--------------------------------------------------------------------------------


<PAGE>   11


--------------------------------------------------------------------------------

Dated:                                        Name of Holder:
      -----------------

                                              (Print)                          
                                                     --------------------------
                                              (By:)                            
                                                     --------------------------
                                              (Name:)
                                              (Title:)

(Signature must conform in all respects to name of holder as specified on the
face of the Warrant)


                                      -11-

<PAGE>   12
         [To be completed and signed only upon transfer of Warrant]

         FOR VALUE RECEIVED, the undersigned hereby sells, assigns and transfers
unto ________________________________ the right represented by the within
Warrant to purchase ____________ shares of Common Stock of Illinois
Superconductor Corporation to which the within Warrant relates and appoints
________________ attorney to transfer said right on the books of Illinois
Superconductor Corporation with full power of substitution in the premises.


Dated:

---------------, ----


                              ---------------------------------------
                              (Signature must conform in all respects to name
                              of holder as specified on the face of the Warrant)


                              ---------------------------------------
                              Address of Transferee

                              ---------------------------------------

                              ---------------------------------------



In the presence of:


--------------------------


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