<PAGE>   1

                                                                     EXHIBIT 4.6

             THIS WARRANT CERTIFICATE IS EXERCISABLE ON OR BEFORE,

            AND VOID AFTER, 5:00 P.M. CENTRAL TIME, JANUARY 23, 2006

                      WARRANTS TO PURCHASE COMMON STOCK OF

                         HYPERTENSION DIAGNOSTICS, INC.

                                   [HDI LOGO]

             INCORPORATED UNDER THE LAWS OF THE STATE OF MINNESOTA

NO. W-                                         CERTIFICATE FOR          WARRANTS


                                                               CUSIP 44914V 12 0


This Certifies That


or assigns, is the owner of the number of Warrants set forth above, each of
which represents the right to purchase from Hypertension Diagnostics, Inc., a
Minnesota corporation (the "Company"), at any time on or before 5:00 P.M.
Central time, January 23, 2006, upon compliance with and subject to the
conditions set forth herein and in the Warrant Agreement hereinafter referred
to, one share (subject to adjustments referred to below) of the Common Stock of
the Company (such shares or other securities or property purchasable upon
exercise of the Warrants being herein called the "Shares"), by surrendering this
Warrant Certificate, with the Purchase Form on the reverse side duly executed,
at the principal office of Firstar Bank, N.A., or its successor, as warrant
agent (the "Warrant Agent"), and by paying in full, in cash or by certified or
official bank check payable to the order of the Company, the exercise price of
$9.00 per share.


     Upon any exercise of less than all the Warrants evidenced by this Warrant
Certificate, there shall be issued to the holder a new Warrant Certificate in
respect of the Warrants as to which this Warrant Certificate was not exercised.

     Upon the surrender for transfer or exchange of any Warrant Certificates,
properly endorsed, to the Warrant Agent, the Warrant Agent at the Company's
expense will issue and deliver to the order of the holder hereof, a new Warrant
Certificate or Warrant Certificates of like tenor, in the name of such holder or
as such holder (upon payment by such holder of any applicable transfer taxes)
may direct, calling in the aggregate on the face or faces thereof for the number
of shares of Common Stock called for on the face hereof.

     The Warrant Certificates are issued only as registered Warrant
Certificates. Until this Warrant Certificate is transferred in the Warrant
Register, the Company and the Warrant Agent may treat the person in whose name
this Warrant Certificate is registered as the absolute owner hereof and of the
Warrants represented hereby for all purposes, notwithstanding any notice to the
contrary.


     This Warrant Certificate is issued under the Warrant Agreement dated as of
January 4, 2001 between the Company and the Warrant Agent. The Warrant Agreement
is hereby incorporated by reference into this Warrant Certificate and this
Warrant Certificate is subject to the terms and provisions contained in said
Warrant Agreement, to all of which terms and provisions the registered holder of
this Warrant Certificate consents by acceptance hereof. Copies of said Warrant
Agreement are on file at the office of the Warrant Agent in Milwaukee,
Wisconsin, and may be obtained by writing to the Warrant Agent.


     The number of Shares receivable upon the exercise of the Warrants
represented by this Warrant Certificate and the exercise price per share are
subject to adjustment upon the happening of certain events specified in the
Warrant Agreement.

     No fractional Shares of the Company's Common Stock will be issued upon the
exercise of Warrants. As to any final fraction of a share which a holder of
Warrants exercised in the same transaction would
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otherwise be entitled to purchase on such exercise, the Company shall pay a cash
adjustment in lieu of any fractional Share determined as provided in the Warrant
Agreement.

     The Warrants may be redeemed at the option of the Company, at any time
commencing after January 23, 2001, and following a period of five (5)
consecutive trading days where the per share closing bid price of the Common
Stock exceeds $13.50, on notice as set forth in the Warrant Agreement, and at a
redemption price equal to $.01 per Warrant. If notice of redemption shall have
been given as provided in the Warrant Agreement and cash sufficient for the
redemption be deposited by the Company for that purpose, the exercise rights of
the Warrants identified for redemption shall expire at the close of business on
such date of redemption unless extended by the Company.

     This Warrant Certificate shall not entitle the holder hereof to any of the
rights of a holder of Common Stock of the Company, including, without
limitation, the right to vote, to receive dividends and other distributions, to
exercise any preemptive right, or to receive any notice of, or to attend
meetings of holders of Common Stock or any other proceedings of the Company.


     This Warrant Certificate shall be void and the Warrants and any rights
represented hereby shall cease unless exercised on or before 5:00 P.M. Central
time on January 23, 2006, unless extended by the Company.


     This Warrant Certificate shall not be valid for any purpose until it shall
have been countersigned by the Warrant Agent.

     WITNESS the facsimile signatures of the Company's duly authorized officers.

                                        HYPERTENSION DIAGNOSTICS, INC.



                                        By: /s/ GREG H. GUETTLER
                                            -----------------------------------
                                                Greg H. Guettler
                                                President



                                        Attest: /s/ CHARLES F. CHESNEY
                                                -------------------------------
                                                    Charles F. Chesney
                                                    Secretary



Dated:


COUNTERSIGNED AND REGISTERED:
FIRSTAR BANK, N.A.
  (Milwaukee, Wisconsin)
  as Warrant Agent

By:
    --------------------------------
    Authorized Officer

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THE CORPORATION WILL FURNISH ANY SHAREHOLDER UPON REQUEST AND WITHOUT CHARGE, A
COPY OF THE ARTICLES OF INCORPORATION AND A FULL STATEMENT OF THE DESIGNATIONS,
PREFERENCES, LIMITATIONS, AND RELATIVE RIGHTS OF THE SHARES OF EACH CLASS OR
SERIES AUTHORIZED TO BE ISSUED, SO FAR AS THEY HAVE BEEN DETERMINED, AND THE
AUTHORITY OF THE BOARD TO DETERMINE THE RELATIVE RIGHTS AND PREFERENCES OF
SUBSEQUENT CLASSES OR SERIES.

TO:  HYPERTENSION DIAGNOSTICS, INC.
     C/O FIRSTAR BANK, N.A.
     WARRANT AGENT

                                 PURCHASE FORM
     (TO BE EXECUTED BY THE REGISTERED HOLDER IN ORDER TO EXERCISE WARRANT
                                 CERTIFICATES)

     The undersigned hereby irrevocably elects to exercise           * of the
Warrants represented by the Warrant Certificate and to purchase for cash the
Shares issuable upon the exercise of said Warrants and requests that
certificates for such Shares shall be issued in the name of

<TABLE>
<S>                                                          <C>
PLEASE INSERT SOCIAL SECURITY OR
OTHER IDENTIFYING NUMBER OF                                  -----------------------------------------------------
REGISTERED HOLDER OF CERTIFICATE                                                 (Print Name)
-----------------------------------
                                                             -----------------------------------------------------
-----------------------------------                                                (Address)

                                                             -----------------------------------------------------
                                                                                   (Address)

Dated:                                                       Signature:
      -----------------------------                                    -------------------------------------------
</TABLE>

* Insert here the number of Warrants evidenced on the face of this Warrant
  Certificate (or, in the case of a partial exercise, the portion thereof being
  exercised), in either case without making any adjustment for additional Common
  Stock or any other securities or property or cash which, pursuant to the
  adjustment provisions referred to in this Warrant Certificate, may be
  deliverable upon exercise.

                                ASSIGNMENT FORM
     (TO BE EXECUTED BY THE REGISTERED HOLDER IN ORDER TO TRANSFER WARRANT
                                 CERTIFICATES)

<TABLE>
<C>                                                          <S>
PLEASE INSERT SOCIAL SECURITY OR                             FOR VALUE RECEIVED, the undersigned hereby sells,
OTHER IDENTIFYING NUMBER OF ASSIGNEE                         assigns and transfers       of the Warrants to
-----------------------------------                          purchase shares of Common Stock represented by this
                                                             Warrant Certificate unto
-----------------------------------
</TABLE>

--------------------------------------------------------------------------------
   (Please print or typewrite name and address, including postal zip code, of
                                   assignee)

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

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

and does hereby irrevocably constitute and appoint
                                                   -----------------------------

Attorney to transfer this Warrant Certificate on the records of the Company with
full power of substitution in the premises.

Dated:                         Signature(s)
      --------------                       -------------------------------------

SIGNATURE(S) GUARANTEED:


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

                                    NOTICE:

    THE SIGNATURE(S) TO THE PURCHASE FORM OR THE ASSIGNMENT FORM MUST CORRESPOND
TO THE NAME(S) AS WRITTEN UPON THE FACE OF THIS WARRANT CERTIFICATE IN EVERY
PARTICULAR WITHOUT ALTERATION OR ENLARGEMENT OR ANY CHANGE WHATSOEVER.