Document:

<PAGE>

                                                                     Exhibit 4.1

THE SECURITIES REPRESENTED BY THIS WARRANT AND THE COMMON STOCK ISSUABLE THEREBY
HAVE NOT BEEN AND WILL NOT BE, EXCEPT AS PROVIDED IN THE REGISTRATION RIGHTS
AGREEMENT REFERRED TO BELOW, REGISTERED UNDER THE SECURITIES ACT OF 1933, AS
AMENDED (THE "SECURITIES ACT"), OR ANY OTHER APPLICABLE SECURITIES LAW AND,
ACCORDINGLY, THE SECURITIES REPRESENTED BY THIS CERTIFICATE MAY NOT BE RESOLD,
PLEDGED, OR OTHERWISE TRANSFERRED, EXCEPT PURSUANT TO AN EFFECTIVE REGISTRATION
STATEMENT UNDER, OR IN A TRANSACTION EXEMPT FROM REGISTRATION UNDER, THE
SECURITIES ACT AND IN ACCORDANCE WITH ANY OTHER APPLICABLE SECURITIES LAWS.

                                    WARRANT

                to Purchase 1,562,500 Shares of Common Stock of

                          MILLER EXPLORATION COMPANY

     This Common Stock Purchase Warrant (the "Warrant") certifies that for value
                                              -------
received, Guardian Energy Management Corp., a Michigan corporation ("Guardian"),
                                                                     --------
or its assigns, is entitled to subscribe for and purchase from Miller
Exploration Company, a Delaware corporation (the "Company"), in whole or in
                                                  -------
part, 1,562,500 shares (the "Warrant Shares") of Common Stock, par value $0.01
                             --------------
per share, of the Company ("Common Stock") at the Exercise Price (as hereinafter
                            ------------
defined), subject, however, to the provisions and upon the terms and conditions
hereinafter set forth This Warrant and all rights hereunder shall expire at 5:00
p.m., Traverse City, Michigan time, on the first  anniversary of the approval of
the Conversion Shares by the stockholders of the Company (the "Termination
Date").

                                   ARTICLE I

                             Exercise of Warrants
                             --------------------

     1.1  Term; Exercise Price.  The Warrant represented hereby may be exercised
          --------------------
by the holder hereof, in whole or in part, at any time and from time to time
after the date hereof until 5:00 p.m., Traverse City, Michigan time, on the
Termination Date (the "Term").  Subject to adjustment as provided in Article IV
                       ----                                          ----------
hereof, the exercise price for shares of Common Stock under this Warrant shall
be $1.35 per share of Common Stock (the "Exercise Price").
                                         --------------

     1.2  Method of Exercise.  To exercise this Warrant, the holder hereof shall
          ------------------
deliver to the Company, at the Warrant Office designated in Section 2.1 hereof,
                                                            -----------
(i) a written notice in the form of the Subscription Notice attached as Exhibit
                                                                        -------
A hereto, stating therein the election of such holder to exercise the Warrants
-
in the manner provided in the Subscription Notice; and (ii) payment in full of
the Exercise Price in cash or by wire transfer or check for all Warrant Shares
purchased hereunder.
<PAGE>

This Warrant shall be deemed to be exercised on the date of receipt by the
Company of the Subscription Notice, accompanied by payment for the Warrant
Shares and surrender of this Warrant, as aforesaid, and such date is referred to
herein as the "Exercise Date". Upon such exercise, the Company shall, as
promptly as practicable and in any event within five business days, issue and
deliver to such holder a certificate or certificates for the full number of the
Warrant Shares purchased by such holder hereunder. As permitted by applicable
law, the person in whose name the certificates for Common Stock are to be issued
shall be deemed to have become a holder of record of such Common Stock on the
Exercise Date and shall be entitled to all of the benefits of such holder on the
Exercise Date, including without limitation the right to receive dividends and
other distributions for which the record date falls on or after the Exercise
Date and to exercise voting rights.

     1.3  Expense and Taxes.  The Company shall pay all expenses and taxes
          -----------------
(including, without limitation, all documentary, stamp, transfer or other
transactional taxes) attributable to the preparation, issuance or delivery of
the Warrant and of the shares of Common Stock issuable upon exercise of the
Warrant.

     1.4  Reservation of Shares.  The Company shall reserve at all times so long
          ---------------------
as the Warrant remain outstanding, free from preemptive rights, out of its
treasury Common Stock or its authorized but unissued shares of Common Stock, or
both, solely for the purpose of effecting the exercise of the Warrant, a
sufficient number of shares of Company Stock to provide for the exercise of the
Warrant.

     1.5  Valid Issuance.  All shares of Common Stock that may be issued upon
          --------------
exercise of the Warrant will, upon issuance by the Company, be duly and validly
issued, fully paid and nonassessable and free from all taxes, liens and charges
with respect to the issuance thereof and, without limiting the generality of the
foregoing, the Company shall take no action or fail to take any action which
will cause a contrary result.

     1.6  No Fractional Share.  The Company shall not be required to issue
          -------------------
fractional shares of Common Stock on the exercise of this Warrant.  If more than
one Warrant shall be presented for exercise at the same time by the same holder,
the number of full shares of Common Stock which shall be issuable upon such
exercise shall be computed on the basis of the aggregate number of whole shares
of Common Stock purchasable on exercise of the Warrant so presented.  If any
fraction of a share of Common Stock would, except for the provisions of this
Section 1.6, be issuable on the exercise of this Warrant, the Company shall pay
-----------
an amount in cash calculated by it to be equal to the price of one share of
Common Stock as quoted on the NASDAQ National Market System at the close of
business on the date of such exercise multiplied by such fraction computed to
the nearest whole cent.

                                      -2-
<PAGE>

                                  ARTICLE II

                                   Transfer
                                   --------

     2.1  Warrant Office.  The Company shall maintain an office for certain
          --------------
purposes specified herein (the "Warrant Office"), which office shall initially
                                --------------
be the Company's offices at 3104 Logan Valley Road, P.O. Box 348, Traverse City,
Michigan 49685-0348, and may subsequently be such other office of the Company or
of any transfer agent of the Common Stock in the continental United States as to
which written notice has previously been given to the holder hereof.  The
Company shall maintain, at the Warrant Office, a register for the Warrants in
which the Company shall record the name and address of the person in whose name
this Warrant has been issued, as well as the name and address of each permitted
assignee of the rights of the registered owner hereof.

     2.2  Limited Right of Transfer.  This Warrant may not be directly or
          -------------------------
indirectly sold, assigned, pledged, hypothecated, encumbered, transferred or
otherwise disposed of without the prior written consent of the Company;
provided, however, that Guardian may assign its interest in this Warrant to one
or more of the entities or individuals listed on Schedule 2.2 hereto upon
receipt by the Company of (a) evidence, in form and substance satisfactory to
the Company, that each such assignee is an "Accredited Investor" as defined
under Rule 501 of the Securities Act, or (b) an opinion of the Company's counsel
that such assignment can be made without registration under the Securities Act.

     2.3  Transfer of Warrant.  The Company agrees to maintain at the Warrant
          -------------------
Office books for the registration and transfer of the Warrant.  Subject to the
provisions of Section 2.2, the Company, from time to time, shall register the
transfer of the Warrant in such books upon surrender of this Warrant at the
Warrant Office properly endorsed or accompanied by appropriate instruments of
transfer and written instructions for transfer satisfactory to the Company.
Upon any such transfer and upon payment by the holder or its transferee of any
applicable transfer taxes, new Warrants shall be issued to the transferee and
the transferor (as their respective interests may appear) and the surrendered
Warrant shall be canceled by the Company.  The Company shall pay all taxes
(other than securities transfer taxes) and all other expenses and charges
payable in connection with the transfer of the Warrant hereunder.

                                  ARTICLE III

                                 Anti-Dilution
                                 -------------

     3.1  Reclassification, Consolidation, Merger or Sale of Assets.  In the
          ---------------------------------------------------------
event that the Company shall be a party to any transaction (including without
limitation (i) any recapitalization or reclassification of the Common Stock
(other than a change in par value, or from par value to no par value, or from no
par value to par value), (ii) any combination or subdivision of the Common Stock
into a lesser or greater number of shares of Common Stock, (iii) any
consolidation of the Company with, or merger of the Company into, any other
person, (iv) any merger of another person into the

                                      -3-
<PAGE>

Company (other than a merger which does not result in a reclassification,
conversion, exchange or cancellation of outstanding shares of Common Stock of
the Company), or (v) any sale or transfer of all or a material amount of all of
the assets of the Company or any compulsory share exchange) pursuant to which
the Common Stock is converted into the right to receive other securities, cash
or other property, then lawful provision shall be made as part of the terms of
such transaction whereby the holder of this Warrant shall receive upon the
exercise hereof the kind and amount of securities, cash and other property
receivable upon such transaction by a holder of the number of shares of Common
Stock for which the Warrant was exercisable immediately prior to such
transaction. The entity formed by such consolidation or resulting from such
merger or which acquires such assets or which acquires the Company's shares, as
the case may be, shall make provision in its certificate or articles of
incorporation or other constituent document to establish such right. The above
provisions shall similarly apply to successive transactions of the foregoing
type.

     3.2  Common Stock Dilutions.  In the event that prior to exercise of this
          ----------------------
Warrant the Company issues or agrees to issue additional shares of Common Stock
pursuant to a stock split or stock dividend, or dividend or distribution of
rights to purchase stock, then the number of shares to be issued pursuant to the
exercise of this Warrant and the Exercise Price therefore shall be adjusted
proportionately.  In the event that prior to the exercise of this Warrant the
Company issues or agrees to issue cash or property pursuant to a dividend or
distribution, this Warrant shall represent the right to acquire, in addition to
the number of shares of Common Stock receivable upon exercise of this Warrant,
and without payment of any additional consideration therefor, the amount of such
cash or property which the holder hereof would have been entitled to receive
pursuant to such dividend or distribution had it been the holder of record of
the Common Stock receivable upon exercise of this Warrant on the record date
therefor.  The Company agrees and covenants that it will not, prior to the
exercise of this Warrant, in connection with any plan for the benefit of
employees or directors (i) issue a number of shares of Common Stock, securities
exercisable for Common Stock or other Common Stock equivalents (the "Plan
Securities") which in the aggregate exceeds fifteen percent (15%) of the total
shares of Common Stock outstanding as of the date thereof, and (ii) of the Plan
Securities issued pursuant to clause (i) of this Section 3.2, issue Plan
Securities which in the aggregate are equal to, convertible into or exercisable
for more than 300,000 shares of Common Stock for consideration, including any
applicable exercise or conversion price, which is below the price quoted for the
Common Stock at the close of business on the day prior to issuance of such Plan
Securities.

     3.3  Prior Notice of Certain Events.  In the event:
          ------------------------------

          (i)    the Company establishes a record date to determine the holders
of Common Stock who are entitled to (A) receive any dividend or other
distribution (other than a dividend payable in shares of Common Stock), (B)
participate in a redemption or repurchase of the then-outstanding shares of
Common Stock, or (C) vote in connection with any of the transactions identified
in clauses (ii), (iii), (iv) or (v) below; or

                                      -4-
<PAGE>

          (ii)   the Company shall (A) declare any dividend (or any other
distribution) on its Common Stock, other than a dividend payable in shares of
Common Stock or (B) declare or authorize a redemption or repurchase of the then-
outstanding shares of Common Stock; or

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

          (iv)   of any reclassification of Common Stock (other than a change in
par value, or from par value to no par value, or from no par value to par
value), or of any other capital reorganization or of any consolidation or merger
to which the Company is a party, or of the sale or transfer of all or
substantially all of the assets of the Company or of any compulsory share
exchange whereby the Common Stock is converted into other securities, cash or
other property; or

          (v)    of the voluntary or involuntary dissolution, liquidation or
winding up of the Company or such event is likely to occur.

then the Company shall cause to be mailed to the holder of this Warrant, at its
address as reflected in the Warrant Office transfer records, a notice stating
(A) the date on which a record (if any) is to be taken with respect to clause
(i) above, (B) the date on which any transaction or event contemplated in any of
clauses (i) through and including clause (v) above is expected to become
effective or the date of the anticipated closing of the public offering, and (C)
the time, if any is fixed, as to when the holders of record of Common Stock
shall be entitled to exchange their shares of Common Stock for securities or
other property deliverable upon any such reclassification, reorganization,
consolidation, merger, sale, transfer, share exchange, dissolution, liquidation
or winding up.  Each notice of an event specified in clause (i) above shall be
sent at least five (5) days prior to the record date specified therein and each
notice of an event specified in clauses (ii) through and including (v) above
shall be delivered at least fifteen (15) days prior to the proposed closing of
such transaction.

                                  ARTICLE IV

                                 Miscellaneous
                                 -------------

     4.1  Entire Agreement.  This Warrant, together with that certain
          ----------------
registration rights agreement of even date herewith by and between the Company
and Guardian (the "Registration Rights Agreement"), contain the entire agreement
between the holder hereof and the Company with respect to the Warrant Shares
purchasable upon exercise hereof and the related transactions and supersedes all
prior arrangements or understandings with respect thereto.

     4.2  Governing Law; Venue.  THIS WARRANT SHALL BE GOVERNED BY AND CONSTRUED
          --------------------
IN ACCORDANCE WITH THE APPLICABLE LAWS OF THE STATE OF

                                      -5-
<PAGE>

DELAWARE AND THE UNITED STATES OF AMERICA FROM TIME TO TIME IN EFFECT.

     4.3  Waiver and Amendment.  Any term or provision of this Warrant may be
          --------------------
waived at any time by the party which is entitled to the benefits thereof and
any term or provision of this Warrant may be amended or supplemented at any time
by agreement of the holder hereof and the Company, except that any waiver of any
term or condition, or any amendment or supplementation, of this Warrant shall be
in writing.  A waiver of any breach or failure to enforce any of the terms or
conditions of this Warrant shall not in any way effect, limit or waiver a
party's rights hereunder at any time to enforce strict compliance thereafter
with every term or condition of this Warrant.

     4.4  Illegality.  In the event that any one or more of the provisions
          ----------
contained in this Warrant shall be determined to be invalid, illegal or
unenforceable in any respect for any reason, the validity, legality and
enforceability of any such provision in any other respect and the remaining
provisions of this Warrant shall not, at the election of the party for whom the
benefit of the provision exists, be in any way impaired.

     4.5  Copy of Warrant.  A copy of this Warrant shall be filed among the
          ---------------
records of the Company.

     4.6  Notice.  Any notice or other document required or permitted to be
          ------
given or delivered to the holder hereof shall be in writing and delivered at, or
sent by telecopy or certified or registered mail to such holder at, the last
address shown on the books of the Company maintained at the Warrant Office for
the registration of this Warrant or at any more recent address of which the
holder hereof shall have notified the Company in writing.  Any notice or other
document required or permitted to be given or delivered to the Company shall be
delivered at, or sent by facsimile transmission or certified or registered mail
to, the Warrant Office, or such other address within the continental United
States of America as shall have been furnished by the Company to the holder of
this Warrant.

     4.7  Limitation of Liability; Not Stockholders.  No provision of this
          -----------------------------------------
Warrant shall be construed as conferring upon the holder hereof the right to
vote, consent, receive dividends or receive notices (other than as herein
expressly provided) in respect of meetings of stockholders for the election of
directors of the Company or any other matter whatsoever as a stockholder of the
Company.  No provision hereof, in the absence of affirmative action by the
holder hereof to purchase shares of Common Stock, and no mere enumeration herein
of the rights or privileges of the holder hereof, shall give rise to any
liability of such holder for the purchase price of any shares of Common Stock or
as a stockholder of the Company, whether such liability is asserted by the
Company or by creditors of the Company.

     4.8  Loss, Destruction, etc. of Warrant.  Upon receipt of evidence
          ----------------------------------
satisfactory to the Company of the loss, theft, mutilation or destruction of
this Warrant, and in the case of any such loss, theft or destruction upon
delivery of a bond of indemnity or such other security in such form and

                                      -6-
<PAGE>

amount as shall be reasonably satisfactory to the Company, or in the event of
such mutilation upon surrender and cancellation of this Warrant, the Company
will make and deliver a new Warrant of like tenor, in lieu of such lost, stolen,
destroyed or mutilated Warrant. Any Warrant issued under the provisions of this
Section 4.8 in lieu of any Warrant alleged to be lost, destroyed or stolen, or
-----------
in lieu of any mutilated Warrant, shall constitute an original contractual
obligation on the part of the Company.  This Warrant shall be promptly canceled
by the Company upon the surrender hereof in connection with any exchange or
replacement.  The Company shall pay all taxes (other than securities transfer
taxes) and all other expenses and charges payable in connection with the
preparation, execution and delivery of Warrants pursuant to this Section 4.8.
                                                                 -----------

     4.9  Compliance with Securities Act and Applicable Law.  The Company shall
          -------------------------------------------------
not be required to transfer this Warrant or to sell or issue Warrant Shares if
such transfer or issuance would constitute a violation by the Company of any
provisions of any law or regulation of any governmental authority.  While the
Company is required to register the resale of the Warrant Shares by holder(s)
pursuant to the Registration Rights Agreement, in the event the Warrant Shares
issuable on exercise of this Warrant are not then registered under the Act, the
Company may imprint the following legend or any other legend which counsel for
the Company considers necessary or advisable to comply with the Securities Act
of 1933:

          "The shares of stock represented by this certificate have not been
          registered under the Securities Act of 1933 or under the securities
          laws of any State and may not be sold, transferred or otherwise
          disposed of except upon such registration or upon receipt by the
          issuer, in form and substance satisfactory to the issuer, of an
          opinion of the issuer's counsel that registration is not required for
          such disposition."

     4.10 Registration Rights.  The Warrants Shares shall be entitled to such
          -------------------
registration rights under the Securities Act and under applicable state
securities laws as are specified in the Registration Rights Agreement.

     4.11 Headings.  The Article and Section and other headings herein are for
          --------
convenience only and are not a part of this Warrant and shall not affect the
interpretation thereof.

               [REMAINDER OF THIS PAGE INTENTIONALLY LEFT BLANK]

                                      -7-
<PAGE>

     IN WITNESS WHEREOF, the Company has caused this Warrant to be signed in its
name.
Dated:    July 11, 2000

                              MILLER EXPLORATION COMPANY

                              By:/s/ Kelly E. Miller
                                 -----------------------------------------------
                              Name: Kelly E. Miller
                                   ---------------------------------------------
                              Title: President
                                    --------------------------------------------

                                      -8-
<PAGE>

                                   EXHIBIT A
                                   ---------

                              SUBSCRIPTION NOTICE
                              -------------------

     The undersigned, the holder of the foregoing Warrant, hereby elects to
exercise purchase rights represented thereby for, and to purchase thereunder,
__________ shares of the Common Stock covered by such Warrant, and herewith
makes payment in full for such shares pursuant to Section 1.2 of such Warrant,
                                                  -----------
and requests that certificates for such shares (and any other securities or
other property issuable upon such exercise) be issued in the name of, and
delivered to ______________________________.

                                        ________________________________________

Dated:  ____________, _____.
<PAGE>

                                 SCHEDULE 2.2

                          LIST OF APPROVED ASSIGNEES
                          --------------------------

                        Jordan Exploration Company LLC
                               Martin G. Lagina
                                Robert M. Boeve
                               Wayne Sterenberg
                                 Craig Tester

          Any Persons (as defined in the Securities Purchase Agreement dated as
          of July 11, 2000 and entered into between Guardian and the Company)
          who control, are controlled by or are under common control with any of
          the above Persons.<PAGE>

                                                                     Exhibit 4.2

THE SECURITIES REPRESENTED BY THIS WARRANT AND THE COMMON STOCK ISSUABLE THEREBY
HAVE NOT BEEN AND WILL NOT BE, EXCEPT AS PROVIDED IN THE REGISTRATION RIGHTS
AGREEMENT REFERRED TO BELOW, REGISTERED UNDER THE SECURITIES ACT OF 1933, AS
AMENDED (THE "SECURITIES ACT"), OR ANY OTHER APPLICABLE SECURITIES LAW AND,
ACCORDINGLY, THE SECURITIES REPRESENTED BY THIS CERTIFICATE MAY NOT BE RESOLD,
PLEDGED, OR OTHERWISE TRANSFERRED, EXCEPT PURSUANT TO AN EFFECTIVE REGISTRATION
STATEMENT UNDER, OR IN A TRANSACTION EXEMPT FROM REGISTRATION UNDER, THE
SECURITIES ACT AND IN ACCORDANCE WITH ANY OTHER APPLICABLE SECURITIES LAWS.

                                    WARRANT

                to Purchase 2,500,000 Shares of Common Stock of

                           MILLER EXPLORATION COMPANY

     This Common Stock Purchase Warrant (the "Warrant") certifies that for value
                                              -------
received, Guardian Energy Management Corp., a Michigan corporation ("Guardian"),
                                                                     --------
or its assigns, is entitled to subscribe for and purchase from Miller
Exploration Company, a Delaware corporation (the "Company"), in whole or in
                                                  -------
part, 2,500,000 shares (the "Warrant Shares") of Common Stock, par value $0.01
                             --------------
per share, of the Company ("Common Stock") at the Exercise Price (as hereinafter
                            ------------
defined), subject, however, to the provisions and upon the terms and conditions
hereinafter set forth This Warrant and all rights hereunder shall expire at 5:00
p.m., Traverse City, Michigan time, on the second  anniversary of the approval
of the Conversion Shares by the stockholders of the Company (the "Termination
Date").

                                   ARTICLE I

                              Exercise of Warrants
                              --------------------

     1.1  Term; Exercise Price.  The Warrant represented hereby may be exercised
          --------------------
by the holder hereof, in whole or in part, at any time and from time to time
after the date hereof until 5:00 p.m., Traverse City, Michigan time, on the
Termination Date (the "Term").  Subject to adjustment as provided in Article IV
                       ----                                          ----------
hereof, the exercise price for shares of Common Stock under this Warrant shall
be $2.50 per share of Common Stock (the "Exercise Price").
                                         --------------

     1.2  Method of Exercise.  To exercise this Warrant, the holder hereof shall
          ------------------
deliver to the Company, at the Warrant Office designated in Section 2.1 hereof,
                                                            -----------
(i) a written notice in the form of the Subscription Notice attached as Exhibit
                                                                        -------
A hereto, stating therein the election of such holder to exercise the Warrants
-
in the manner provided in the Subscription Notice; and (ii) payment in full of
the Exercise Price in cash or by wire transfer or check for all Warrant Shares
purchased hereunder.
<PAGE>

This Warrant shall be deemed to be exercised on the date of receipt by the
Company of the Subscription Notice, accompanied by payment for the Warrant
Shares and surrender of this Warrant, as aforesaid, and such date is referred to
herein as the "Exercise Date". Upon such exercise, the Company shall, as
               -------------
promptly as practicable and in any event within five business days, issue and
deliver to such holder a certificate or certificates for the full number of the
Warrant Shares purchased by such holder hereunder. As permitted by applicable
law, the person in whose name the certificates for Common Stock are to be issued
shall be deemed to have become a holder of record of such Common Stock on the
Exercise Date and shall be entitled to all of the benefits of such holder on the
Exercise Date, including without limitation the right to receive dividends and
other distributions for which the record date falls on or after the Exercise
Date and to exercise voting rights.

     1.3  Expense and Taxes.  The Company shall pay all expenses and taxes
          -----------------
(including, without limitation, all documentary, stamp, transfer or other
transactional taxes) attributable to the preparation, issuance or delivery of
the Warrant and of the shares of Common Stock issuable upon exercise of the
Warrant.

     1.4  Reservation of Shares.  The Company shall reserve at all times so long
          ---------------------
as the Warrant remain outstanding, free from preemptive rights, out of its
treasury Common Stock or its authorized but unissued shares of Common Stock, or
both, solely for the purpose of effecting the exercise of the Warrant, a
sufficient number of shares of Company Stock to provide for the exercise of the
Warrant.

     1.5  Valid Issuance.  All shares of Common Stock that may be issued upon
          --------------
exercise of the Warrant will, upon issuance by the Company, be duly and validly
issued, fully paid and nonassessable and free from all taxes, liens and charges
with respect to the issuance thereof and, without limiting the generality of the
foregoing, the Company shall take no action or fail to take any action which
will cause a contrary result.

     1.6  No Fractional Share.  The Company shall not be required to issue
          -------------------
fractional shares of Common Stock on the exercise of this Warrant.  If more than
one Warrant shall be presented for exercise at the same time by the same holder,
the number of full shares of Common Stock which shall be issuable upon such
exercise shall be computed on the basis of the aggregate number of whole shares
of Common Stock purchasable on exercise of the Warrant so presented.  If any
fraction of a share of Common Stock would, except for the provisions of this

Section 1.6, be issuable on the exercise of this Warrant, the Company shall pay
-----------
an amount in cash calculated by it to be equal to the price of one share of
Common Stock as quoted on the NASDAQ National Market System at the close of
business on the date of such exercise multiplied by such fraction computed to
the nearest whole cent.

                                      -2-
<PAGE>

                                   ARTICLE II

                                    Transfer
                                    --------

     2.1  Warrant Office.  The Company shall maintain an office for certain
          --------------
purposes specified herein (the "Warrant Office"), which office shall initially
                                --------------
be the Company's offices at 3104 Logan Valley Road, P.O. Box 348, Traverse City,
Michigan 49685-0348, and may subsequently be such other office of the Company or
of any transfer agent of the Common Stock in the continental United States as to
which written notice has previously been given to the holder hereof.  The
Company shall maintain, at the Warrant Office, a register for the Warrants in
which the Company shall record the name and address of the person in whose name
this Warrant has been issued, as well as the name and address of each permitted
assignee of the rights of the registered owner hereof.

     2.2  Limited Right of Transfer.  This Warrant may not be directly or
          -------------------------
indirectly sold, assigned, pledged, hypothecated, encumbered, transferred or
otherwise disposed of without the prior written consent of the Company;
provided, however, that Guardian may assign its interest in this Warrant to one
or more of the entities or individuals listed on Schedule 2.2 hereto upon
receipt by the Company of (a) evidence, in form and substance satisfactory to
the Company, that each such assignee is an "Accredited Investor" as defined
under Rule 501 of the Securities Act, or (b) an opinion of the Company's counsel
that such assignment can be made without registration under the Securities Act.

     2.3  Transfer of Warrant.  The Company agrees to maintain at the Warrant
          -------------------
Office books for the registration and transfer of the Warrant.  Subject to the
provisions of Section 2.2, the Company, from time to time, shall register the
transfer of the Warrant in such books upon surrender of this Warrant at the
Warrant Office properly endorsed or accompanied by appropriate instruments of
transfer and written instructions for transfer satisfactory to the Company.
Upon any such transfer and upon payment by the holder or its transferee of any
applicable transfer taxes, new Warrants shall be issued to the transferee and
the transferor (as their respective interests may appear) and the surrendered
Warrant shall be canceled by the Company.  The Company shall pay all taxes
(other than securities transfer taxes) and all other expenses and charges
payable in connection with the transfer of the Warrant hereunder.

                                  ARTICLE III

                                 Anti-Dilution
                                 -------------

     3.1  Reclassification, Consolidation, Merger or Sale of Assets.  In the
          ---------------------------------------------------------
event that the Company shall be a party to any transaction (including without
limitation (i) any recapitalization or reclassification of the Common Stock
(other than a change in par value, or from par value to no par value, or from no
par value to par value), (ii) any combination or subdivision of the Common Stock
into a lesser or greater number of shares of Common Stock, (iii) any
consolidation of the Company with, or merger of the Company into, any other
person, (iv) any merger of another person into the

                                      -3-
<PAGE>

Company (other than a merger which does not result in a reclassification,
conversion, exchange or cancellation of outstanding shares of Common Stock of
the Company), or (v) any sale or transfer of all or a material amount of all of
the assets of the Company or any compulsory share exchange) pursuant to which
the Common Stock is converted into the right to receive other securities, cash
or other property, then lawful provision shall be made as part of the terms of
such transaction whereby the holder of this Warrant shall receive upon the
exercise hereof the kind and amount of securities, cash and other property
receivable upon such transaction by a holder of the number of shares of Common
Stock for which the Warrant was exercisable immediately prior to such
transaction. The entity formed by such consolidation or resulting from such
merger or which acquires such assets or which acquires the Company's shares, as
the case may be, shall make provision in its certificate or articles of
incorporation or other constituent document to establish such right. The above
provisions shall similarly apply to successive transactions of the foregoing
type.

     3.2  Common Stock Dilutions. In the event that prior to exercise of this
          ----------------------
Warrant the Company issues or agrees to issue additional shares of Common Stock
pursuant to a stock split or stock dividend, or dividend or distribution of
rights to purchase stock, then the number of shares to be issued pursuant to the
exercise of this Warrant and the Exercise Price therefore shall be adjusted
proportionately.  In the event that prior to the exercise of this Warrant the
Company issues or agrees to issue cash or property pursuant to a dividend or
distribution, this Warrant shall represent the right to acquire, in addition to
the number of shares of Common Stock receivable upon exercise of this Warrant,
and without payment of any additional consideration therefor, the amount of such
cash or property which the holder hereof would have been entitled to receive
pursuant to such dividend or distribution had it been the holder of record of
the Common Stock receivable upon exercise of this Warrant on the record date
therefor.  The Company agrees and covenants that it will not, prior to the
exercise of this Warrant, in connection with any plan for the benefit of
employees or directors (i) issue a number of shares of Common Stock, securities
exercisable for Common Stock or other Common Stock equivalents (the "Plan
Securities") which in the aggregate exceeds fifteen percent (15%) of the total
shares of Common Stock outstanding as of the date thereof, and (ii) of the Plan
Securities issued pursuant to clause (i) of this Section 3.2, issue Plan
Securities which in the aggregate are equal to, convertible into or exercisable
for more than 300,000 shares of Common Stock for consideration, including any
applicable exercise or conversion price, which is below the price quoted for the
Common Stock at the close of business on the day prior to issuance of such Plan
Securities.

     3.3  Prior Notice of Certain Events.  In the event:
          ------------------------------

          (i) the Company establishes a record date to determine the holders of
Common Stock who are entitled to (A) receive any dividend or other distribution
(other than a dividend payable in shares of Common Stock), (B) participate in a
redemption or repurchase of the then-outstanding shares of Common Stock, or (C)
vote in connection with any of the transactions identified in clauses
(ii),(iii), (iv) or (v) below; or

                                      -4-
<PAGE>

          (ii) the Company shall (A) declare any dividend (or any other
distribution) on its Common Stock, other than a dividend payable in shares of
Common Stock or (B) declare or authorize a redemption or repurchase of the then-
outstanding shares of Common Stock; or

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

          (iv) of any reclassification of Common Stock (other than a change in
par value, or from par value to no par value, or from no par value to par
value), or of any other capital reorganization or of any consolidation or merger
to which the Company is a party, or of the sale or transfer of all or
substantially all of the assets of the Company or of any compulsory share
exchange whereby the Common Stock is converted into other securities, cash or
other property; or

          (v) of the voluntary or involuntary dissolution, liquidation or
winding up of the Company or such event is likely to occur.

then the Company shall cause to be mailed to the holder of this Warrant, at its
address as reflected in the Warrant Office transfer records, a notice stating
(A) the date on which a record (if any) is to be taken with respect to clause
(i) above, (B) the date on which any transaction or event contemplated in any of
clauses (i) through and including clause (v) above is expected to become
effective or the date of the anticipated closing of the public offering, and (C)
the time, if any is fixed, as to when the holders of record of Common Stock
shall be entitled to exchange their shares of Common Stock for securities or
other property deliverable upon any such reclassification, reorganization,
consolidation, merger, sale, transfer, share exchange, dissolution, liquidation
or winding up.  Each notice of an event specified in clause (i) above shall be
sent at least five (5) days prior to the record date specified therein and each
notice of an event specified in clauses (ii) through and including (v) above
shall be delivered at least fifteen (15) days prior to the proposed closing of
such transaction.

                                   ARTICLE IV

                                 Miscellaneous
                                 -------------

     4.1  Entire Agreement.  This Warrant, together with that certain
          ----------------
registration rights agreement of even date herewith by and between the Company
and Guardian (the "Registration Rights Agreement"), contain the entire agreement
between the holder hereof and the Company with respect to the Warrant Shares
purchasable upon exercise hereof and the related transactions and supersedes all
prior arrangements or understandings with respect thereto.

     4.2  Governing Law; Venue.  THIS WARRANT SHALL BE GOVERNED BY AND CONSTRUED
          --------------------
IN ACCORDANCE WITH THE APPLICABLE LAWS OF THE STATE OF

                                      -5-
<PAGE>

DELAWARE AND THE UNITED STATES OF AMERICA FROM TIME TO TIME IN EFFECT.

     4.3  Waiver and Amendment.  Any term or provision of this Warrant may be
          --------------------
waived at any time by the party which is entitled to the benefits thereof and
any term or provision of this Warrant may be amended or supplemented at any time
by agreement of the holder hereof and the Company, except that any waiver of any
term or condition, or any amendment or supplementation, of this Warrant shall be
in writing.  A waiver of any breach or failure to enforce any of the terms or
conditions of this Warrant shall not in any way effect, limit or waiver a
party's rights hereunder at any time to enforce strict compliance thereafter
with every term or condition of this Warrant.

     4.4  Illegality.  In the event that any one or more of the provisions
          ----------
contained in this Warrant shall be determined to be invalid, illegal or
unenforceable in any respect for any reason, the validity, legality and
enforceability of any such provision in any other respect and the remaining
provisions of this Warrant shall not, at the election of the party for whom the
benefit of the provision exists, be in any way impaired.

     4.5  Copy of Warrant.  A copy of this Warrant shall be filed among the
          ---------------
records of the Company.

     4.6  Notice.  Any notice or other document required or permitted to be
          ------
given or delivered to the holder hereof shall be in writing and delivered at, or
sent by telecopy or certified or registered mail to such holder at, the last
address shown on the books of the Company maintained at the Warrant Office for
the registration of this Warrant or at any more recent address of which the
holder hereof shall have notified the Company in writing.  Any notice or other
document required or permitted to be given or delivered to the Company shall be
delivered at, or sent by facsimile transmission or certified or registered mail
to, the Warrant Office, or such other address within the continental United
States of America as shall have been furnished by the Company to the holder of
this Warrant.

     4.7  Limitation of Liability; Not Stockholders.  No provision of this
          -----------------------------------------
Warrant shall be construed as conferring upon the holder hereof the right to
vote, consent, receive dividends or receive notices (other than as herein
expressly provided) in respect of meetings of stockholders for the election of
directors of the Company or any other matter whatsoever as a stockholder of the
Company.  No provision hereof, in the absence of affirmative action by the
holder hereof to purchase shares of Common Stock, and no mere enumeration herein
of the rights or privileges of the holder hereof, shall give rise to any
liability of such holder for the purchase price of any shares of Common Stock or
as a stockholder of the Company, whether such liability is asserted by the
Company or by creditors of the Company.

     4.8  Loss, Destruction, etc. of Warrant.  Upon receipt of evidence
          ----------------------------------
satisfactory to the Company of the loss, theft, mutilation or destruction of
this Warrant, and in the case of any such loss, theft or destruction upon
delivery of a bond of indemnity or such other security in such form and

                                      -6-
<PAGE>

amount as shall be reasonably satisfactory to the Company, or in the event of
such mutilation upon surrender and cancellation of this Warrant, the Company
will make and deliver a new Warrant of like tenor, in lieu of such lost, stolen,
destroyed or mutilated Warrant. Any Warrant issued under the provisions of this
Section 4.8 in lieu of any Warrant alleged to be lost, destroyed or stolen, or
-----------
in lieu of any mutilated Warrant, shall constitute an original contractual
obligation on the part of the Company.  This Warrant shall be promptly canceled
by the Company upon the surrender hereof in connection with any exchange or
replacement.  The Company shall pay all taxes (other than securities transfer
taxes) and all other expenses and charges payable in connection with the
preparation, execution and delivery of Warrants pursuant to this Section 4.8.
                                                                 -----------

     4.9  Compliance with Securities Act and Applicable Law.  The Company shall
          -------------------------------------------------
not be required to transfer this Warrant or to sell or issue Warrant Shares if
such transfer or issuance would constitute a violation by the Company of any
provisions of any law or regulation of any governmental authority.  While the
Company is required to register the resale of the Warrant Shares by holder(s)
pursuant to the Registration Rights Agreement, in the event the Warrant Shares
issuable on exercise of this Warrant are not then registered under the Act, the
Company may imprint the following legend or any other legend which counsel for
the Company considers necessary or advisable to comply with the Securities Act
of 1933:

          "The shares of stock represented by this certificate have not been
          registered under the Securities Act of 1933 or under the securities
          laws of any State and may not be sold, transferred or otherwise
          disposed of except upon such registration or upon receipt by the
          issuer, in form and substance satisfactory to the issuer, of an
          opinion of the issuer's counsel that registration is not required for
          such disposition."

     4.1  Registration Rights.  The Warrants Shares shall be entitled to such
          -------------------
registration rights under the Securities Act and under applicable state
securities laws as are specified in the Registration Rights Agreement.

     4.1  Headings.  The Article and Section and other headings herein are for
          --------
convenience only and are not a part of this Warrant and shall not affect the
interpretation thereof.

               [REMAINDER OF THIS PAGE INTENTIONALLY LEFT BLANK]

                                      -7-
<PAGE>

     IN WITNESS WHEREOF, the Company has caused this Warrant to be signed in its
name.

Dated:    July 11, 2000

                              MILLER EXPLORATION COMPANY

                              By: /s/ Kelly E. Miller
                                 --------------------------
                              Name: Kelly E. Miller
                                   ------------------------
                              Title: President
                                    -----------------------

                                      -8-
<PAGE>

                                   EXHIBIT A
                                   ---------

                              SUBSCRIPTION NOTICE
                              -------------------

     The undersigned, the holder of the foregoing Warrant, hereby elects to
exercise purchase rights represented thereby for, and to purchase thereunder,
__________ shares of the Common Stock covered by such Warrant, and herewith
makes payment in full for such shares pursuant to Section 1.2 of such Warrant,
                                                  -----------
and requests that certificates for such shares (and any other securities or
other property issuable upon such exercise) be issued in the name of, and
delivered to ______________________________.

                                                -----------------------------
Dated:  ____________, _____.

                                      -9-
<PAGE>

                                  SCHEDULE 2.2

                           LIST OF APPROVED ASSIGNEES
                           --------------------------

                         Jordan Exploration Company LLC
                                Martin G. Lagina
                                Robert M. Boeve
                                Wayne Sterenberg
                                  Craig Tester

          Any Persons (as defined in the Securities Purchase Agreement
          dated as of July 11, 2000 and entered into between Guardian
          and the Company) who control, are controlled by or are under
          common control with any of the above Persons.

                                      -10-

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