EX-4.1



 Exhibit 4.1 

ENTEROMEDICS INC. 

CERTIFICATE OF DESIGNATION OF PREFERENCES, 

RIGHTS AND LIMITATIONS 

OF 
 SERIES A CONVERTIBLE
PREFERRED STOCK 
 PURSUANT TO SECTION 151 OF THE 

DELAWARE GENERAL CORPORATION LAW 

JANUARY     , 2017 

The undersigned, Dan W. Gladney and Scott P. Youngstrom, do hereby certify that: 

1. They are the President and Secretary, respectively, of EnteroMedics Inc., a Delaware corporation (the “Corporation”). 

2. The Corporation is authorized to issue 5,000,000 shares of preferred stock, none of which have been issued. 

3. The following resolutions were duly adopted by the board of directors of the Corporation (the “Board of Directors”): 

WHEREAS, the certificate of incorporation of the Corporation provides for a class of its authorized stock known as preferred stock, consisting
of 5,000,000 shares, $0.01 par value per share, issuable from time to time in one or more series; 
 WHEREAS, the Board of Directors is
authorized to fix the dividend rights, dividend rate, voting rights, conversion rights, rights and terms of redemption and liquidation preferences of any wholly unissued series of preferred stock and the number of shares constituting any series and
the designation thereof, of any of them; and 
 WHEREAS, it is the desire of the Board of Directors, pursuant to its authority as aforesaid,
to fix the rights, preferences, restrictions and other matters relating to a series of the preferred stock, which shall consist of, except as otherwise set forth in the Underwriting Agreement, up to
                     shares of the preferred stock which the Corporation has the authority to issue, as follows: 

NOW, THEREFORE, BE IT RESOLVED, that the Board of Directors does hereby provide for the issuance of a series of preferred stock for cash or
exchange of other securities, rights or property and does hereby fix and determine the rights, preferences, restrictions and other matters relating to such series of preferred stock as follows: 

  
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 TERMS OF PREFERRED STOCK 

Section 1. Definitions. For the purposes hereof, the following terms shall have the following meanings: 

“Affiliate” means any Person that, directly or indirectly through one or more intermediaries, controls or is
controlled by or is under common control with a Person, as such terms are used in and construed under Rule 405 of the Securities Act. 

“Alternate Consideration” shall have the meaning set forth in Section 7(e). 

“Beneficial Ownership Limitation” shall have the meaning set forth in Section 6(d). 

“Business Day” means any day except any Saturday, any Sunday, any day which is a federal legal holiday in the
United States or any day on which banking institutions in the State of New York are authorized or required by law or other governmental action to close. 

“Buy-In” shall have the meaning set forth in Section 6(c)(iv). 

“Commission” means the United States Securities and Exchange Commission. 

“Common Stock” means the Corporation’s common stock, par value $0.01 per share, and stock of any other
class of securities into which such securities may hereafter be reclassified or changed. 
 “Common Stock
Equivalents” means any securities of the Corporation or the Subsidiaries which would entitle the holder thereof to acquire at any time Common Stock, including, without limitation, any debt, preferred stock, rights, options, warrants or
other instrument that is at any time convertible into or exercisable or exchangeable for, or otherwise entitles the holder thereof to receive, Common Stock. 

“Conversion Amount” means the sum of the Stated Value at issue. 

“Conversion Date” shall have the meaning set forth in Section 6(a). 

“Conversion Price” shall have the meaning set forth in Section 6(b). 

“Conversion Shares” means, collectively, the shares of Common Stock issuable upon conversion of the shares of
Preferred Stock in accordance with the terms hereof. 
 “Equity Conditions” means, during the period in
question, (a) the Corporation shall have duly honored all conversions scheduled to occur or occurring by virtue of one or more Notices of Conversion of the applicable Holder on or prior to the dates so


  
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requested or required, if any, (b) the Corporation shall have paid all liquidated damages and other amounts owing to the applicable Holder in respect of the Preferred Stock, (c)(i) there is
an effective registration statement pursuant to which the Corporation may issue Conversion Shares or (ii) all of the Conversion Shares may be issued to the Holder pursuant to Section 3(a)(9) of the Securities Act and immediately resold
without restriction, (d) the Common Stock is trading on a Trading Market and all of the Conversion Shares are listed or quoted for trading on such Trading Market (and the Corporation believes, in good faith, that trading of the Common Stock on
a Trading Market will continue uninterrupted for the foreseeable future), (e) there is a sufficient number of authorized, but unissued and otherwise unreserved, shares of Common Stock for the issuance of all of the shares then issuable pursuant
to the Preferred Stock then outstanding, (f) the issuance of the shares in question to the applicable Holder would not violate the limitations set forth in Section 6(d) herein, (g) there has been no public announcement of a pending or
proposed Fundamental Transaction that has not been consummated and (h) the applicable Holder is not in possession of any information provided by the Corporation, any of its Subsidiaries, or any of their officers, directors, employees, agents or
Affiliates, that constitutes, or may constitute, material non-public information. 
 “Exchange Act” means
the Securities Exchange Act of 1934, as amended, and the rules and regulations promulgated thereunder. 

“Fundamental Transaction” shall have the meaning set forth in Section 7(e). 

“GAAP” means United States generally accepted accounting principles. 

“Holder” shall have the meaning given such term in Section 2. 

“Liquidation” shall have the meaning set forth in Section 5. 

“New York Courts” shall have the meaning set forth in Section 8(d). 

“Notice of Conversion” shall have the meaning set forth in Section 6(a). 

“Original Issue Date” means the date of the first issuance of any shares of the Preferred Stock regardless of
the number of transfers of any particular shares of Preferred Stock and regardless of the number of certificates which may be issued to evidence such Preferred Stock. 

“Person” means an individual or corporation, partnership, trust, incorporated or unincorporated association,
joint venture, limited liability company, joint stock company, government (or an agency or subdivision thereof) or other entity of any kind. 

“Preferred Stock” shall have the meaning set forth in Section 2. 

“Representative” means Ladenburg Thalmann & Co. Inc. 

  
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 “Securities Act” means the Securities Act of 1933, as amended,
and the rules and regulations promulgated thereunder. 
 “Share Delivery Date” shall have the meaning set
forth in Section 6(c). 
 “Stated Value” shall have the meaning set forth in Section 2, as the
same may be increased pursuant to Section 3. 
 “Subsidiary” means any subsidiary of the Corporation
and shall, where applicable, also include any direct or indirect subsidiary of the Corporation formed or acquired after the date hereof. 

“Successor Entity” shall have the meaning set forth in Section 7(e). 

“Trading Day” means a day on which the principal Trading Market is open for business. 

“Trading Market” means any of the following markets or exchanges on which the Common Stock is listed or quoted
for trading on the date in question: the NYSE MKT, the Nasdaq Capital Market, the Nasdaq Global Market, the Nasdaq Global Select Market, or the New York Stock Exchange (or any successors to any of the foregoing). 

“Transfer Agent” means Wells Fargo Bank, N.A., the current transfer agent of the Corporation, with a mailing
address 1110 Centre Pointe Curve, Suite 101, Mendota Heights, Minnesota 55120 and a facsimile number of (651) 450-4078, and any successor transfer agent of the Corporation. 

“Underwriting Agreement” means the underwriting agreement, dated as of January __, 2017, among the Corporation
and the Representative as representative of the underwriters named therein, as amended, modified or supplemented from time to time in accordance with its terms. 

“VWAP” means, for any date, the price determined by the first of the following clauses that applies:
(a) if the Common Stock is then listed or quoted on a Trading Market, the daily volume weighted average price of the Common Stock for such date (or the nearest preceding date) on the principal Trading Market on which the Common Stock is then
listed or quoted as reported by Bloomberg L.P. (based on a Trading Day from 9:30 a.m. (New York City time) to 4:02 p.m. (New York City time)), (b) if OTCQB or OTCQX is not a Trading Market, the volume weighted average price of the Common Stock
for such date (or the nearest preceding date) on OTCQB or OTCQX as applicable, (c) if the Common Stock is not then listed or quoted for trading on OTCQB or OTCQX and if prices for the Common Stock are then reported in the “Pink
Sheets” published by OTC Markets Group, Inc. (or a similar organization or agency succeeding to its functions of reporting prices), the most recent bid price per share of the Common Stock so reported, or (d) in all other cases, the fair
market value of a share of Common Stock as determined by an independent appraiser selected in good faith by the holders of a majority in interest of the Warrants then outstanding and reasonably acceptable to the Corporation, the fees and expenses of
which shall be paid by the Corporation. 

  
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 Section 2. Designation, Amount and Par Value. The series of preferred stock
shall be designated as the Corporation’s Series A Convertible Preferred Stock (the “Preferred Stock”) and the number of shares so designated shall be up to
             (which shall not be subject to increase without the written consent of all of the holders of the Preferred Stock (each, a “Holder” and collectively, the
“Holders”)). Each share of Preferred Stock shall have a par value of $0.01 per share and a stated value equal to $1,000 (the “Stated Value”). The shares of Preferred Stock shall initially be issued and maintained in
the form of securities held in book-entry form and the Depository Trust Company or its nominee (“DTC”) shall initially be the sole registered holder of the shares of Preferred Stock. 

Section 3. Dividends. Except for stock dividends or distributions for which adjustments are to be made pursuant to
Section 7, Holders shall be entitled to receive, and the Corporation shall pay, dividends on shares of Preferred Stock equal (on an as-if-converted-to-Common-Stock basis) to and in the same form as dividends actually paid on shares of the
Common Stock when, as and if such dividends are paid on shares of the Common Stock. No other dividends shall be paid on shares of Preferred Stock. 

Section 4. Voting Rights. Except as otherwise provided herein or as otherwise required by law, the Preferred Stock shall
have no voting rights. However, as long as any shares of Preferred Stock are outstanding, the Corporation shall not, without the affirmative vote of the Holders of a majority of the then outstanding shares of the Preferred Stock, (a) alter or
change adversely the powers, preferences or rights given to the Preferred Stock or alter or amend this Certificate of Designation, (b) amend its certificate of incorporation or other charter documents in any manner that adversely affects any
rights of the Holders, (c) increase the number of authorized shares of Preferred Stock, or (d) enter into any agreement with respect to any of the foregoing. 

Section 5. Liquidation. Upon any liquidation, dissolution or winding-up of the Corporation, whether voluntary or
involuntary (a “Liquidation”), the Holders shall be entitled to receive out of the assets, whether capital or surplus, of the Corporation an amount equal to the par value, plus any accrued and unpaid dividends thereon, for each
share of Preferred Stock before any distribution or payment shall be made to the holders of the Common Stock, and if the assets of the Corporation shall be insufficient to pay in full such amounts, then the entire assets to be distributed to the
Holders shall be ratably distributed among the Holders in accordance with the respective amounts that would be payable on such shares if all amounts payable thereon were paid in full; and thereafter, the Holders shall be entitled to receive out of
the assets, whether capital or surplus, of the Corporation the same amount that a holder of Common Stock would receive if the Preferred Stock were fully converted (disregarding for such purposes any conversion limitations hereunder) to Common Stock
which amounts shall be paid pari passu with all holders of Common Stock. The Corporation shall mail written notice of any such Liquidation, not less than 45 days prior to the payment date stated therein, to each Holder. 

Section 6. Conversion. 

a) Conversions at Option of Holder. Each share of Preferred Stock shall be convertible, at any time and from time to
time from and after the Original Issue Date at 

  
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the option of the Holder thereof, into that number of shares of Common Stock (subject to the limitations set forth in Section 6(d)) determined by dividing the Stated Value of such share of
Preferred Stock by the Conversion Price. Holders shall effect conversions by providing the Corporation with the form of conversion notice attached hereto as Annex A (a “Notice of Conversion”). Each Notice of Conversion shall
specify the number of shares of Preferred Stock to be converted, the number of shares of Preferred Stock owned prior to the conversion at issue, the number of shares of Preferred Stock owned subsequent to the conversion at issue and the date on
which such conversion is to be effected, which date may not be prior to the date the applicable Holder delivers by facsimile such Notice of Conversion to the Corporation (such date, the “Conversion Date”). Upon delivery of the
Notice of Conversion, the Holder shall be deemed for all corporate purposes to have become the holder of record of the Conversion Shares with respect to which the shares of Preferred Stock have been converted irrespective of the date of delivery of
the Conversion Shares, provided that the Holder shall deliver such converted shares of Preferred Stock to the Transfer Agent via the DTC’s Deposit/Withdrawal at Custodian system within two Trading Days of delivery of the Notice of Conversion.
If no Conversion Date is specified in a Notice of Conversion, the Conversion Date shall be the date that such Notice of Conversion to the Corporation is deemed delivered hereunder. No ink-original Notice of Conversion shall be required, nor shall
any medallion guarantee (or other type of guarantee or notarization) of any Notice of Conversion form be required. The calculations and entries set forth in the Notice of Conversion shall control in the absence of manifest or mathematical error. To
effect conversions of shares of Preferred Stock, a Holder shall not be required to surrender the certificate(s) representing the shares of Preferred Stock to the Corporation unless all of the shares of Preferred Stock represented thereby are so
converted, in which case such Holder shall deliver the certificate representing such shares of Preferred Stock promptly following the Conversion Date at issue. Shares of Preferred Stock converted into Common Stock or redeemed in accordance with the
terms hereof shall be canceled and shall not be reissued. 
 Without limiting the rights and remedies of a holder of Preferred Stock
hereunder and without limiting the right of a Holder to deliver a Notice of Conversion to the Corporation, a holder whose interest in the shares of Preferred Stock is a beneficial interest in certificate(s) representing the shares of Preferred Stock
held in book-entry form through DTC (or another established clearing corporation performing similar functions), may effect conversions made pursuant to this Section 6(a) by delivering to DTC (or such other clearing corporation, as applicable) the
appropriate instruction form for conversion, complying with the procedures to effect conversions that are required by DTC (or such other clearing corporation, as applicable). 

b) Conversion Price. The conversion price for the Preferred Stock shall equal
$            , subject to adjustment herein (the “Conversion Price”). 

c) Mechanics of Conversion 

i. Delivery of Conversion Shares Upon Conversion. Not later than the earlier of (i) three (3) Trading Days
and (ii) the number of Trading Days comprising the Standard Settlement Period (as defined below) after each Conversion Date (the “Share Delivery Date”), the Corporation shall deliver, or cause to be delivered, to the converting
Holder (A) the number of Conversion Shares being acquired upon the conversion of the Preferred Stock, which Conversion Shares shall be free of restrictive legends and trading restrictions and (B) a bank check in the amount of accrued and
unpaid dividends, if any. The Corporation shall use its best efforts to deliver the Conversion Shares required to be delivered by the Corporation under this Section 6 electronically through the Depository Trust Company or another established
clearing corporation performing similar functions. As used herein, “Standard Settlement Period” means the standard settlement period, expressed in a number of Trading Days, on the Corporation’s primary Trading Market with
respect to the Common Stock as in effect on the date of delivery of the Notice of Conversion. 

  
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 ii. Failure to Deliver Conversion Shares. If, in the case of any Notice of
Conversion, such Conversion Shares are not delivered to or as directed by the applicable Holder by the Share Delivery Date, the Holder shall be entitled to elect by written notice to the Corporation at any time on or before its receipt of such
Conversion Shares, to rescind such Conversion, in which event the Corporation shall promptly return to the Holder any original Preferred Stock certificate delivered to the Corporation and the Holder shall promptly return to the Corporation the
Conversion Shares issued to such Holder pursuant to the rescinded Notice of Conversion. 
 iii. Obligation Absolute;
Partial Liquidated Damages. The Corporation’s obligation to issue and deliver the Conversion Shares upon conversion of Preferred Stock in accordance with the terms hereof are absolute and unconditional, irrespective of any action or
inaction by a Holder to enforce the same, any waiver or consent with respect to any provision hereof, the recovery of any judgment against any Person or any action to enforce the same, or any setoff, counterclaim, recoupment, limitation or
termination, or any breach or alleged breach by such Holder or any other Person of any obligation to the Corporation or any violation or alleged violation of law by such Holder or any other person, and irrespective of any other circumstance which
might otherwise limit such obligation of the Corporation to such Holder in connection with the issuance of such Conversion Shares; provided, however, that such delivery shall not operate as a waiver by the Corporation of any such
action that the Corporation may have against such Holder. In the event a Holder shall elect to convert any or all of the Stated Value of its Preferred Stock, the Corporation may not refuse conversion based on any claim that such Holder or any one
associated or affiliated with such Holder has been engaged in any violation of law, agreement or for any other reason, unless an injunction from a court, on notice to Holder, restraining and/or enjoining conversion of all or part of the Preferred
Stock of such Holder shall have been sought and obtained, and the Corporation posts a surety bond for the benefit of such Holder in the amount of 150% of the Stated Value of Preferred Stock which is subject to the injunction, which bond shall remain
in effect until the completion of arbitration/litigation of the underlying dispute and the proceeds of which shall be payable to such Holder to the extent it obtains judgment. In the absence of such injunction, the Corporation shall issue Conversion
Shares and, if applicable, cash, upon a properly noticed conversion. If the Corporation fails to deliver to a Holder such Conversion Shares pursuant to Section 6(c)(i) by the Share Delivery Date applicable to such conversion, the Corporation
shall pay to such Holder, in cash, as liquidated damages and not as a penalty, for each $5,000 of Stated Value of Preferred Stock being converted, $50 per Trading Day (increasing to $100 per Trading Day on the third Trading Day and increasing to
$200 per Trading Day on the sixth Trading Day after such damages begin to accrue) for each Trading Day after the Share Delivery Date until such Conversion Shares are delivered or Holder rescinds such conversion. Nothing herein shall limit a
Holder’s right to pursue actual damages for the Corporation’s failure to deliver Conversion Shares within the period specified herein and such Holder 

  
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shall have the right to pursue all remedies available to it hereunder, at law or in equity including, without limitation, a decree of specific performance and/or injunctive relief. The exercise
of any such rights shall not prohibit a Holder from seeking to enforce damages pursuant to any other Section hereof or under applicable law. 

iv. Compensation for Buy-In on Failure to Timely Deliver Conversion Shares Upon Conversion. In addition to any other
rights available to the Holder, if the Corporation fails for any reason to deliver to a Holder the applicable Conversion Shares by the Share Delivery Date pursuant to Section 6(c)(i), and if after such Share Delivery Date such Holder is
required by its brokerage firm to purchase (in an open market transaction or otherwise), or the Holder’s brokerage firm otherwise purchases, shares of Common Stock to deliver in satisfaction of a sale by such Holder of the Conversion Shares
which such Holder was entitled to receive upon the conversion relating to such Share Delivery Date (a “Buy-In”), then the Corporation shall (A) pay in cash to such Holder (in addition to any other remedies available to or
elected by such Holder) the amount, if any, by which (x) such Holder’s total purchase price (including any brokerage commissions) for the Common Stock so purchased exceeds (y) the product of (1) the aggregate number of shares of
Common Stock that such Holder was entitled to receive from the conversion at issue multiplied by (2) the actual sale price at which the sell order giving rise to such purchase obligation was executed (including any brokerage commissions) and
(B) at the option of such Holder, either reissue (if surrendered) the shares of Preferred Stock equal to the number of shares of Preferred Stock submitted for conversion (in which case, such conversion shall be deemed rescinded) or deliver to
such Holder the number of shares of Common Stock that would have been issued if the Corporation had timely complied with its delivery requirements under Section 6(c)(i). For example, if a Holder purchases shares of Common Stock having a total
purchase price of $11,000 to cover a Buy-In with respect to an attempted conversion of shares of Preferred Stock with respect to which the actual sale price of the Conversion Shares (including any brokerage commissions) giving rise to such purchase
obligation was a total of $10,000 under clause (A) of the immediately preceding sentence, the Corporation shall be required to pay such Holder $1,000. The Holder shall provide the Corporation written notice indicating the amounts payable to
such Holder in respect of the Buy-In and, upon request of the Corporation, evidence of the amount of such loss. Nothing herein shall limit a Holder’s right to pursue any other remedies available to it hereunder, at law or in equity including,
without limitation, a decree of specific performance and/or injunctive relief with respect to the Corporation’s failure to timely deliver Conversion Shares upon conversion of the shares of Preferred Stock as required pursuant to the terms
hereof. 
 v. Reservation of Shares Issuable Upon Conversion. The Corporation covenants that it will at all times
reserve and keep available out of its authorized and unissued shares of Common Stock for the sole purpose of issuance upon conversion of the Preferred Stock as herein provided, free from preemptive rights


  
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or any other actual contingent purchase rights of Persons other than the Holder (and the other holders of the Preferred Stock), not less than such aggregate number of shares of the Common Stock
as shall be issuable (taking into account the adjustments and restrictions of Section 7) upon the conversion of the then outstanding shares of Preferred Stock. The Corporation covenants that all shares of Common Stock that shall be so issuable
shall, upon issue, be duly authorized, validly issued, fully paid and nonassessable. 
 vi. Fractional Shares. No
fractional shares or scrip representing fractional shares shall be issued upon the conversion of the Preferred Stock. As to any fraction of a share which the Holder would otherwise be entitled to purchase upon such conversion, the Corporation shall
at its election, either pay a cash adjustment in respect of such final fraction in an amount equal to such fraction multiplied by the Conversion Price or round up to the next whole share. 

vii. Transfer Taxes and Expenses. The issuance of Conversion Shares on conversion of this Preferred Stock shall be made
without charge to any Holder for any documentary stamp or similar taxes that may be payable in respect of the issue or delivery of such Conversion Shares, provided that the Corporation shall not be required to pay any tax that may be payable in
respect of any transfer involved in the issuance and delivery of any such Conversion Shares upon conversion in a name other than that of the Holders of such shares of Preferred Stock and the Corporation shall not be required to issue or deliver such
Conversion Shares unless or until the Person or Persons requesting the issuance thereof shall have paid to the Corporation the amount of such tax or shall have established to the satisfaction of the Corporation that such tax has been paid. The
Corporation shall pay all Transfer Agent fees required for same-day processing of any Notice of Conversion and all fees to the Depository Trust Company (or another established clearing corporation performing similar functions) required for same-day
electronic delivery of the Conversion Shares. 
 d) Beneficial Ownership Limitation. The Corporation shall not effect
any conversion of the Preferred Stock, and a Holder shall not have the right to convert any portion of the Preferred Stock, to the extent that, after giving effect to the conversion set forth on the applicable Notice of Conversion, such Holder
(together with such Holder’s Affiliates, and any Persons acting as a group together with such Holder or any of such Holder’s Affiliates (such Persons, “Attribution Parties”)) would beneficially own in excess of the Beneficial
Ownership Limitation (as defined below). For purposes of the foregoing sentence, the number of shares of Common Stock beneficially owned by such Holder and its Affiliates and Attribution Parties shall include the number of shares of Common
Stock issuable upon conversion of the Preferred Stock with respect to which such determination is being made, but shall exclude the number of shares of Common Stock which are issuable upon (i) conversion of the remaining, unconverted Stated
Value of Preferred Stock beneficially owned by such Holder or any of its Affiliates or Attribution Parties and (ii) exercise or conversion of the unexercised or unconverted portion of any other securities of the Corporation subject to a
limitation on conversion or 

  
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exercise analogous to the limitation contained herein (including, without limitation, the Preferred Stock) beneficially owned by such Holder or any of its Affiliates or Attribution
Parties. Except as set forth in the preceding sentence, for purposes of this Section 6(d), beneficial ownership shall be calculated in accordance with Section 13(d) of the Exchange Act and the rules and regulations promulgated
thereunder. To the extent that the limitation contained in this Section 6(d) applies, the determination of whether the Preferred Stock is convertible (in relation to other securities owned by such Holder together with any Affiliates and
Attribution Parties) and of how many shares of Preferred Stock are convertible shall be in the sole discretion of such Holder, and the submission of a Notice of Conversion shall be deemed to be such Holder’s determination of whether the shares
of Preferred Stock may be converted (in relation to other securities owned by such Holder together with any Affiliates and Attribution Parties) and how many shares of the Preferred Stock are convertible, in each case subject to the Beneficial
Ownership Limitation. To ensure compliance with this restriction, each Holder will be deemed to represent to the Corporation each time it delivers a Notice of Conversion that such Notice of Conversion has not violated the restrictions set forth in
this paragraph and the Corporation shall have no obligation to verify or confirm the accuracy of such determination. In addition, a determination as to any group status as contemplated above shall be determined in accordance with Section 13(d)
of the Exchange Act and the rules and regulations promulgated thereunder. For purposes of this Section 6(d), in determining the number of outstanding shares of Common Stock, a Holder may rely on the number of outstanding shares of Common Stock
as stated in the most recent of the following: (i) the Corporation’s most recent periodic or annual report filed with the Commission, as the case may be, (ii) a more recent public announcement by the Corporation or (iii) a more
recent written notice by the Corporation or the Transfer Agent setting forth the number of shares of Common Stock outstanding. Upon the written or oral request (which may be via email) of a Holder, the Corporation shall within two
(2) Trading Days confirm orally and in writing to such Holder the number of shares of Common Stock then outstanding. In any case, the number of outstanding shares of Common Stock shall be determined after giving effect to the conversion or
exercise of securities of the Corporation, including the Preferred Stock, by such Holder or its Affiliates or Attribution Parties since the date as of which such number of outstanding shares of Common Stock was reported. The “Beneficial
Ownership Limitation” shall be 4.99% (or, upon election by a Holder prior to the issuance of any shares of Preferred Stock, up to 9.99%) of the number of shares of the Common Stock outstanding immediately after giving effect to the issuance
of shares of Common Stock issuable upon conversion of Preferred Stock held by the applicable Holder. A Holder, upon notice to the Corporation, may increase or decrease the Beneficial Ownership Limitation provisions of this Section 6(d)
applicable to its Preferred Stock provided that the Beneficial Ownership Limitation in no event exceeds 9.99% of the number of shares of the Common Stock outstanding immediately after giving effect to the issuance of shares of Common Stock upon
conversion of this Preferred Stock held by the Holder and the provisions of this Section 6(d) shall continue to apply. Any such increase in the Beneficial Ownership Limitation will not be effective until the 61st day after such notice is delivered to the Corporation and shall only apply to such Holder and no other Holder. The provisions of this paragraph shall be construed and implemented in a manner


  
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otherwise than in strict conformity with the terms of this Section 6(d) to correct this paragraph (or any portion hereof) which may be defective or inconsistent with the intended Beneficial
Ownership Limitation contained herein or to make changes or supplements necessary or desirable to properly give effect to such limitation. The limitations contained in this paragraph shall apply to a successor holder of Preferred Stock. 

e) Forced Conversion. Notwithstanding anything herein to the contrary, if after the Original Issue Date, the VWAP for
each of any thirty (30) consecutive Trading Day period, which thirty (30) consecutive Trading Day period shall have commenced only after the Original Issue Date (the “Threshold Period”), exceeds
$            1 (subject to adjustment for forward and reverse stock splits, recapitalizations, stock dividends and the like after
the Original Issue Date) and (ii) the average daily dollar trading volume for such Threshold Period exceeds $500,000 per Trading Day, the Corporation may, within one (1) Trading Day after the end of any such Threshold Period, deliver a
written notice to all Holders (a “Forced Conversion Notice” and the date such notice is delivered to all Holders, the “Forced Conversion Notice Date”) to cause each Holder to convert all or part of such
Holder’s Preferred Stock (as specified in such Forced Conversion Notice) pursuant to Section 6, it being agreed that the “Conversion Date” for purposes of Section 6 shall be deemed to occur on the third Trading Day following
the Forced Conversion Notice Date (such third Trading Day, the “Forced Conversion Date”). The Corporation may not deliver a Forced Conversion Notice, and any Forced Conversion Notice delivered by the Corporation shall not be
effective, unless all of the Equity Conditions have been met on each Trading Day during the applicable Threshold Period through and including the later of the Forced Conversion Date and the Trading Day after the date that the Conversion Shares
issuable pursuant to such conversion are actually delivered to the Holders pursuant to the Forced Conversion Notice. Any Forced Conversion Notices shall be applied ratably to all of the Holders based on the then outstanding shares of Preferred
Stock. For purposes of clarification, a Forced Conversion shall be subject to all of the provisions of Section 6, including, without limitation, the provisions requiring payment of liquidated damages and limitations on conversions. 

Section 7. Certain Adjustments. 

a) Stock Dividends and Stock Splits. If the Corporation, at any time while this Preferred Stock is outstanding:
(i) pays a stock dividend or otherwise makes a distribution or distributions payable in shares of Common Stock on shares of Common Stock or any other Common Stock Equivalents (which, for avoidance of doubt, shall not include any shares of
Common Stock issued by the Corporation upon conversion of, or payment of a dividend on, this Preferred Stock), (ii) subdivides outstanding shares of Common Stock into a larger number of shares, (iii) combines (including by way of a reverse
stock split) outstanding shares of Common Stock into a smaller number of shares, or (iv) issues, in the event of a reclassification of shares of the Common Stock, any shares of capital stock of the Corporation, then the Conversion Price shall
be multiplied by a 
  

	1 	 300% of the Conversion Price 



  
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fraction of which the numerator shall be the number of shares of Common Stock (excluding any treasury shares of the Corporation) outstanding immediately before such event, and of which the
denominator shall be the number of shares of Common Stock outstanding immediately after such event. Any adjustment made pursuant to this Section 7(a) 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, combination or re-classification. 

b) [RESERVED] 

c) Subsequent Rights Offerings. In addition to any adjustments pursuant to Section 7(a) above, if at any time the
Corporation grants, issues or sells any Common Stock Equivalents or rights to purchase stock, warrants, securities or other property pro rata to the record holders of any class of shares of Common Stock (the “Purchase Rights”), then
the Holder will be entitled to acquire, upon the terms applicable to such Purchase Rights, the aggregate Purchase Rights which the Holder could have acquired if the Holder had held the number of shares of Common Stock acquirable upon complete
conversion of such Holder’s Preferred Stock (without regard to any limitations on exercise hereof, including without limitation, the Beneficial Ownership Limitation) immediately before the date on which a record is taken for the grant, issuance
or sale of such Purchase Rights, or, if no such record is taken, the date as of which the record holders of shares of Common Stock are to be determined for the grant, issue or sale of such Purchase Rights (provided, however, to the extent that the
Holder’s right to participate in any such Purchase Right would result in the Holder exceeding the Beneficial Ownership Limitation, then the Holder shall not be entitled to participate in such Purchase Right to such extent (or beneficial
ownership of such shares of Common Stock as a result of such Purchase Right to such extent) and such Purchase Right to such extent shall be held in abeyance for the Holder until such time, if ever, as its right thereto would not result in the Holder
exceeding the Beneficial Ownership Limitation). 
 d) Pro Rata Distributions. During such time as this Preferred
Stock is outstanding, if the Corporation declares or makes any dividend or other distribution of its assets (or rights to acquire its assets) to holders of shares of Common Stock, by way of return of capital or otherwise (including, without
limitation, any distribution of cash, stock or other securities, property or options by way of a dividend, spin off, reclassification, corporate rearrangement, scheme of arrangement or other similar transaction) (a “Distribution”),
at any time after the issuance of this Preferred Stock, then, in each such case, the Holder shall be entitled to participate in such Distribution to the same extent that the Holder would have participated therein if the Holder had held the number of
shares of Common Stock acquirable upon complete conversion of this Preferred Stock (without regard to any limitations on conversion hereof, including without limitation, the Beneficial Ownership Limitation) immediately before the date of which a
record is taken for such Distribution, or, if no such record is taken, the date as of which the record holders of shares of Common Stock are to be determined for the participation in such Distribution (provided, however, to the extent
that the Holder’s right 

  
 12 








 
to participate in any such Distribution would result in the Holder exceeding the Beneficial Ownership Limitation, then the Holder shall not be entitled to participate in such Distribution to such
extent (or in the beneficial ownership of any shares of Common Stock as a result of such Distribution to such extent) and the portion of such Distribution shall be held in abeyance for the benefit of the Holder until such time, if ever, as its right
thereto would not result in the Holder exceeding the Beneficial Ownership Limitation). 
 e) Fundamental Transaction.
If, at any time while this Preferred Stock is outstanding, (i) the Corporation, directly or indirectly, in one or more related transactions effects any merger or consolidation of the Corporation with or into another Person, (ii) the
Corporation, directly or indirectly, effects any sale, lease, license, assignment, transfer, conveyance or other disposition of all or substantially all of its assets in one or a series of related transactions, (iii) any, direct or indirect,
purchase offer, tender offer or exchange offer (whether by the Corporation or another Person) is completed pursuant to which holders of Common Stock are permitted to sell, tender or exchange their shares for other securities, cash or property and
has been accepted by the holders of 50% or more of the outstanding Common Stock, (iv) the Corporation, directly or indirectly, in one or more related transactions effects any reclassification, reorganization or recapitalization of the Common
Stock or any compulsory share exchange pursuant to which the Common Stock is effectively converted into or exchanged for other securities, cash or property, or (v) the Corporation, directly or indirectly, in one or more related transactions
consummates a stock or share purchase agreement or other business combination (including, without limitation, a reorganization, recapitalization, spin-off or scheme of arrangement) with another Person whereby such other Person acquires more than 50%
of the outstanding shares of Common Stock (not including any shares of Common Stock held by the other Person or other Persons making or party to, or associated or affiliated with the other Persons making or party to, such stock or share purchase
agreement or other business combination) (each a “Fundamental Transaction”), then, upon any subsequent conversion of this Preferred Stock, the Holder shall have the right to receive, for each Conversion Share that would have been
issuable upon such conversion immediately prior to the occurrence of such Fundamental Transaction (without regard to any limitation in Section 6(d) on the conversion of this Preferred Stock), the number of shares of Common Stock of the
successor or acquiring corporation or of the Corporation, if it is the surviving corporation, and any additional consideration (the “Alternate Consideration”) receivable as a result of such Fundamental Transaction by a holder of the
number of shares of Common Stock for which this Preferred Stock is convertible immediately prior to such Fundamental Transaction (without regard to any limitation in Section 6(d) on the conversion of this Preferred Stock). For purposes of any
such conversion, the determination of the Conversion Price shall be appropriately adjusted to apply to such Alternate Consideration based on the amount of Alternate Consideration issuable in respect of one share of Common Stock in such Fundamental
Transaction, and the Corporation shall apportion the Conversion Price among the Alternate Consideration in a reasonable manner reflecting the relative value of any different components of the Alternate Consideration. If holders of Common Stock are
given any choice as to the securities, cash or property to be received in a Fundamental Transaction, then the Holder shall be given the same choice as to the Alternate Consideration it receives upon any


  
 13 








 
conversion of this Preferred Stock following such Fundamental Transaction. To the extent necessary to effectuate the foregoing provisions, any successor to the Corporation or surviving entity in
such Fundamental Transaction shall file a new Certificate of Designation with the same terms and conditions and issue to the Holders new preferred stock consistent with the foregoing provisions and evidencing the Holders’ right to convert such
preferred stock into Alternate Consideration. The Corporation shall cause any successor entity in a Fundamental Transaction in which the Corporation is not the survivor (the “Successor Entity”) to assume in writing all of the
obligations of the Corporation under this Certificate of Designation in accordance with the provisions of this Section 7(e) pursuant to written agreements in form and substance reasonably satisfactory to the Holder and approved by the Holder
(without unreasonable delay) prior to such Fundamental Transaction and shall, at the option of the holder of this Preferred Stock, deliver to the Holder in exchange for this Preferred Stock a security of the Successor Entity evidenced by a written
instrument substantially similar in form and substance to this Preferred Stock which is convertible for a corresponding number of shares of capital stock of such Successor Entity (or its parent entity) equivalent to the shares of Common Stock
acquirable and receivable upon conversion of this Preferred Stock (without regard to any limitations on the conversion of this Preferred Stock) prior to such Fundamental Transaction, and with a conversion price which applies the conversion price
hereunder to such shares of capital stock (but taking into account the relative value of the shares of Common Stock pursuant to such Fundamental Transaction and the value of such shares of capital stock, such number of shares of capital stock and
such conversion price being for the purpose of protecting the economic value of this Preferred Stock immediately prior to the consummation of such Fundamental Transaction), and which is reasonably satisfactory in form and substance to the Holder.
Upon the occurrence of any such Fundamental Transaction, the Successor Entity shall succeed to, and be substituted for (so that from and after the date of such Fundamental Transaction, the provisions of this Certificate of Designation referring to
the “Corporation” shall refer instead to the Successor Entity), and may exercise every right and power of the Corporation and shall assume all of the obligations of the Corporation under this Certificate of Designation with the same effect
as if such Successor Entity had been named as the Corporation herein. 
 f) Calculations. All calculations under this
Section 7 shall be made to the nearest cent or the nearest 1/100th of a share, as the case may be. For purposes of this Section 7, the number of shares of Common Stock deemed to be issued and outstanding as of a given date shall be the sum
of the number of shares of Common Stock (excluding any treasury shares of the Corporation) issued and outstanding. 
 g)
Notice to the Holders. 
 i. Adjustment to Conversion Price. Whenever the Conversion Price is adjusted
pursuant to any provision of this Section 7, the Corporation shall promptly deliver to each Holder a notice setting forth the Conversion Price after such adjustment and setting forth a brief statement of the facts requiring such adjustment.


  
 14 








 ii. Notice to Allow Conversion by Holder. If (A) the Corporation
shall declare a dividend (or any other distribution in whatever form) on the Common Stock, (B) the Corporation shall declare a special nonrecurring cash dividend on or a redemption of the Common Stock, (C) the Corporation shall authorize
the granting to all holders of the Common Stock of rights or warrants to subscribe for or purchase any shares of capital stock of any class or of any rights, (D) the approval of any stockholders of the Corporation shall be required in
connection with any reclassification of the Common Stock, any consolidation or merger to which the Corporation is a party, any sale or transfer of all or substantially all of the assets of the Corporation, or any compulsory share exchange whereby
the Common Stock is converted into other securities, cash or property or (E) the Corporation shall authorize the voluntary or involuntary dissolution, liquidation or winding up of the affairs of the Corporation, then, in each case, the
Corporation shall cause to be filed at each office or agency maintained for the purpose of conversion of this Preferred Stock, and shall cause to be delivered to each Holder at its last address as it shall appear upon the stock books of the
Corporation, at least twenty (20) 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 the 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 the Common Stock of record shall be entitled to exchange
their shares of the Common Stock for securities, cash or other property deliverable upon such reclassification, consolidation, merger, sale, transfer or share exchange, provided that the failure to deliver such notice or any defect therein or in the
delivery thereof shall not affect the validity of the corporate action required to be specified in such notice. To the extent that any notice provided hereunder constitutes, or contains, material, non-public information regarding the Corporation or
any of the Subsidiaries, the Corporation shall simultaneously file such notice with the Commission pursuant to a Current Report on Form 8-K. The Holder shall remain entitled to convert the Conversion Amount of this Preferred Stock (or any part
hereof) during the 20-day period commencing on the date of such notice through the effective date of the event triggering such notice except as may otherwise be expressly set forth herein. 

Section 8. Miscellaneous. 

a) Notices. Any and all notices or other communications or deliveries to be provided by the Holders hereunder
including, without limitation, any Notice of Conversion, shall be in writing and delivered personally, by facsimile, or sent by a nationally recognized overnight courier service, addressed to the Corporation, at the address set forth above
Attention: Chief Financial Officer, facsimile: (651) 634-3212, 

  
 15 








 
email: syoungstrom@enteromedics.com or such other facsimile number, e-mail address or address as the Corporation may specify for such purposes by notice to the Holders delivered in accordance
with this Section 11. Any and all notices or other communications or deliveries to be provided by the Corporation hereunder shall be in writing and delivered personally, by facsimile, by email, or sent by a nationally recognized overnight
courier service addressed to each Holder at the facsimile number or address of such Holder appearing on the books of the Corporation. Any notice or other communication or deliveries hereunder shall be deemed given and effective on the earliest of
(i) the date of transmission, if such notice or communication is delivered via facsimile at the facsimile number or email at the email address set forth in this Section prior to 5:30 p.m. (New York City time) on any date, (ii) the next
Trading Day after the date of transmission, if such notice or communication is delivered via facsimile at the facsimile number or email at the email address set forth in this Section on a day that is not a Trading Day or later than 5:30 p.m. (New
York City time) on any Trading Day, (iii) the second Trading Day following the date of mailing, if sent by U.S. nationally recognized overnight courier service, or (iv) upon actual receipt by the party to whom such notice is required to be
given. 
 b) Absolute Obligation. Except as expressly provided herein, no provision of this Certificate of
Designation shall alter or impair the obligation of the Corporation, which is absolute and unconditional, to pay liquidated damages and accrued dividends, as applicable, on the shares of Preferred Stock at the time, place, and rate, and in the coin
or currency, herein prescribed. 
 c) Lost or Mutilated Preferred Stock Certificate. If a Holder’s Preferred
Stock certificate shall be mutilated, lost, stolen or destroyed, the Corporation shall execute and deliver, in exchange and substitution for and upon cancellation of a mutilated certificate, or in lieu of or in substitution for a lost, stolen or
destroyed certificate, a new certificate for the shares of Preferred Stock so mutilated, lost, stolen or destroyed, but only upon receipt of evidence of such loss, theft or destruction of such certificate, and of the ownership hereof reasonably
satisfactory to the Corporation. 
 d) Governing Law. All questions concerning the construction, validity,
enforcement and interpretation of this Certificate of Designation shall be governed by and construed and enforced in accordance with the internal laws of the State of Delaware, without regard to the principles of conflict of laws thereof. Each party
agrees that all legal proceedings concerning the interpretation, enforcement and defense of the transactions contemplated by this Certificate of Designation (whether brought against a party hereto or its respective Affiliates, directors, officers,
shareholders, employees or agents) shall be commenced in the state and federal courts sitting in the City of New York, Borough of Manhattan (the “New York Courts”). Each party hereto hereby irrevocably submits to the exclusive
jurisdiction of the New York Courts for the adjudication of any dispute hereunder or in connection herewith or with any transaction contemplated hereby or discussed herein, and hereby irrevocably waives, and agrees not to assert in any suit, action
or proceeding, any claim that it is not personally subject to the jurisdiction of such New York Courts, or such New York Courts are improper or inconvenient venue for such proceeding. Each party hereby irrevocably waives personal


  
 16 








 
service of process and consents to process being served in any such suit, action or proceeding by mailing a copy thereof via registered or certified mail or overnight delivery (with evidence of
delivery) to such party at the address in effect for notices to it under this Certificate of Designation and agrees that such service shall constitute good and sufficient service of process and notice thereof. Nothing contained herein shall be
deemed to limit in any way any right to serve process in any other manner permitted by applicable law. Each party hereto hereby irrevocably waives, to the fullest extent permitted by applicable law, any and all right to trial by jury in any legal
proceeding arising out of or relating to this Certificate of Designation or the transactions contemplated hereby. If any party shall commence an action or proceeding to enforce any provisions of this Certificate of Designation, then the prevailing
party in such action or proceeding shall be reimbursed by the other party for its attorneys’ fees and other costs and expenses incurred in the investigation, preparation and prosecution of such action or proceeding. 

e) Waiver. Any waiver by the Corporation or a Holder of a breach of any provision of this Certificate of Designation
shall not operate as or be construed to be a waiver of any other breach of such provision or of any breach of any other provision of this Certificate of Designation or a waiver by any other Holders. The failure of the Corporation or a Holder to
insist upon strict adherence to any term of this Certificate of Designation on one or more occasions shall not be considered a waiver or deprive that party (or any other Holder) of the right thereafter to insist upon strict adherence to that term or
any other term of this Certificate of Designation on any other occasion. Any waiver by the Corporation or a Holder must be in writing. 

f) Severability. If any provision of this Certificate of Designation is invalid, illegal or unenforceable, the balance
of this Certificate of Designation shall remain in effect, and if any provision is inapplicable to any Person or circumstance, it shall nevertheless remain applicable to all other Persons and circumstances. If it shall be found that any interest or
other amount deemed interest due hereunder violates the applicable law governing usury, the applicable rate of interest due hereunder shall automatically be lowered to equal the maximum rate of interest permitted under applicable law. 

g) Next Business Day. Whenever any payment or other obligation hereunder shall be due on a day other than a Business
Day, such payment shall be made on the next succeeding Business Day. 
 h) Headings. The headings contained herein
are for convenience only, do not constitute a part of this Certificate of Designation and shall not be deemed to limit or affect any of the provisions hereof. 

i) Status of Converted or Redeemed Preferred Stock. If any shares of Preferred Stock shall be converted, redeemed or
reacquired by the Corporation, such shares shall resume the status of authorized but unissued shares of preferred stock and shall no longer be designated as Series A Convertible Preferred Stock. 

********************* 

  
 17 








 RESOLVED, FURTHER, that the Chairman, the president or any vice-president, and the secretary or any assistant
secretary, of the Corporation be and they hereby are authorized and directed to prepare and file this Certificate of Designation of Preferences, Rights and Limitations in accordance with the foregoing resolution and the provisions of Delaware law.

 IN WITNESS WHEREOF, the undersigned have executed this Certificate as of the date first set forth above. 

 

													
							
	By:	 	 	 	 	 		 	By:	 	 	 	 
		 	Name:	 	Dan W. Gladney	 		 		 	Name:	 	Scott P. Youngstrom
		 	Title:	 	President and Chief Executive Officer	 		 		 	Title:	 	Chief Financial Officer and Chief Compliance Officer


  
 [Signature Page to
EnteroMedics Series A Convertible Preferred Stock Certificate of Designation] 








 ANNEX A 

NOTICE OF CONVERSION 
 [TO BE
EXECUTED BY THE REGISTERED HOLDER IN ORDER TO CONVERT SHARES OF PREFERRED STOCK] 
 The undersigned hereby elects to convert the number of shares of Series
A Convertible Preferred Stock indicated below into shares of common stock, par value $0.01 per share (the “Common Stock”), of EnteroMedics Inc., a Delaware corporation (the “Corporation”), according to the
conditions hereof, as of the date written below. If shares of Common Stock are to be issued in the name of a Person other than the undersigned, the undersigned will pay all transfer taxes payable with respect thereto. No fee will be charged to the
Holders for any conversion, except for any such transfer taxes. 
 Conversion calculations: 

 

			
		
	
        Date to Effect Conversion:
	  	 


			
		
	
        Number of shares of Preferred Stock 
owned prior to Conversion:
	  	 


			
		
	
        Number of shares of Preferred Stock 
to be Converted:
	  	 


			
		
	
        Stated Value of shares of Preferred 
Stock to be Converted:
	  	 


			
		
	
        Number of shares of Common Stock 
to be Issued:
	  	 


			
		
	
        Applicable Conversion Price:
	  	 


			
		
	
        Number of shares of Preferred Stock 
subsequent to Conversion:
	  	 


			
		
	         Address for Delivery:
	  	  



			
	         or

        DWAC Instructions:
	  	


			
		
	         Broker no:
	  	  



			
		
	         Account no:
	  	  


  

					
	[HOLDER]
		
	By:	 	 
		 	Name:	 	
		 	Title: