Form of Director Restricted Stock Unit Agreement under the BioCardia 2016 Equity Incentive Plan

Exhibit 4.1

[Director Deferred Settlement—Fixed Date]

BIOCARDIA, INC.

2016 EQUITY INCENTIVE PLAN

RESTRICTED STOCK UNIT AGREEMENT

Unless otherwise defined herein, the terms defined in the BioCardia, Inc. 2016 Equity Incentive Plan (the “Plan”) will have the same defined meanings in this Restricted Stock Unit Agreement (the “Award Agreement”), which includes the Notice of Restricted Stock Unit Grant (the “Notice of Grant”) and the Terms and Conditions of Restricted Stock Unit Grant, attached hereto as Exhibit A.

NOTICE OF RESTRICTED STOCK UNIT GRANT

Participant Name:                         

Address:                    

Participant has been granted the right to receive an Award of Restricted Stock Units, subject to the terms and conditions of the Plan and this Award Agreement, as follows:

Vesting Schedule:

Subject to any acceleration provisions contained in the Plan or set forth below, the Restricted Stock Units will vest in accordance with the following schedule:

100% of the Restricted Stock Units will be fully vested on the Date of Grant.

Settlement Date:

Shares shall be issued on the earliest to occur of: (1) the two (2) year anniversary of the Grant Date; (2) Participant’s separation from service (within the meaning of Code Section 409A); (3) a Change in Control; or (4) Participant’s death (as applicable, the “Settlement Date”). In all instances, subject to the terms of this Award Agreement, the Shares will be issued within sixty (60) days of the applicable Settlement Date and if the sixty (60) day period straddles two calendar years, Participant will not under any circumstances be permitted, directly or indirectly, to designate the taxable year in which the Restricted Stock Units are settled.

By Participant’s signature and the signature of the representative of BioCardia, Inc. (the “Company”) below, Participant and the Company agree that this Award of Restricted Stock Units is granted under and governed by the terms and conditions of the Plan and this Award Agreement. Participant has reviewed the Plan and this Award Agreement in their entirety, has had an opportunity to obtain the advice of counsel prior to executing this Award Agreement and fully understands all provisions of the Plan and Award Agreement. Participant hereby agrees to accept as binding, conclusive and final all decisions or interpretations of the Administrator upon any questions relating to the Plan and Award Agreement. Participant further agrees to notify the Company upon any change in the residence address indicated below.

EXHIBIT A

TERMS AND CONDITIONS OF RESTRICTED STOCK UNIT GRANT

1.     Grant. The Company hereby grants to the individual named in the Notice of Grant (the “Participant”) under the Plan an Award of Restricted Stock Units, subject to all of the terms and conditions in this Award Agreement and the Plan, which is incorporated herein by reference. Subject to Section 19(c) of the Plan, in the event of a conflict between the terms and conditions of the Plan and the terms and conditions of this Award Agreement, the terms and conditions of the Plan will prevail.

(a)     General Rule. Each Restricted Stock Unit represents the right to receive a Share on the Settlement Date (to the extent vested). Prior to the Settlement Date, such Restricted Stock Unit will represent an unsecured obligation of the Company, payable (if at all) only from the general assets of the Company. Subject to Section 2(b), any Restricted Stock Units will be paid to Participant (or in the event of Participant’s death, to his or her properly designated beneficiary or estate) in whole Shares as soon as practicable after the Settlement Date, but in each such case within sixty (60) days following the Settlement Date. If the sixty (60) day period straddles two calendar years, Participant will not under any circumstances be permitted, directly or indirectly, to designate the taxable year in which the Restricted Stock Units are settled.

(b)     Section 409A. Notwithstanding anything in the Plan or this Award Agreement to the contrary, if the Settlement Date is Participant’s “separation from service” within the meaning of Section 409A, as determined by the Company, other than due to Participant’s death, and if (x) Participant is a “specified employee” within the meaning of Section 409A on that date, and (y) the payment of such accelerated Restricted Stock Units will result in the imposition of additional tax under Section 409A if paid to Participant on or within the six (6) month period following Participant’s separation from service, then the payment of the Restricted Stock Units will not be made until the date six (6) months and one (1) day following the date of Participant’s separation from service, unless Participant dies following his or her separation from service, in which case, the Restricted Stock Units will be paid in Shares to Participant’s estate as soon as practicable following his or her death. It is the intent of this Award Agreement to comply with the requirements of Section 409A so that none of the Restricted Stock Units provided under this Agreement or Shares issuable thereunder will be subject to the additional tax imposed under Section 409A, and any ambiguities herein will be interpreted to so comply. Each payment payable under this Award Agreement is intended to constitute a separate payment for purposes of Treasury Regulation Section 1.409A-2(b)(2). For purposes of this Agreement, “Section 409A” means Section 409A of the Code and any proposed, temporary or final Treasury Regulations and Internal Revenue Service guidance thereunder, as each may be amended from time to time.

3.     Death of Participant. Any distribution or delivery to be made to Participant under this Award Agreement will, if Participant is then deceased, be made to Participant’s designated beneficiary, or if no beneficiary survives Participant, the administrator or executor of Participant’s estate. Any such transferee must furnish the Company with (a) written notice of his or her status as transferee, and (b) evidence satisfactory to the Company to establish the validity of the transfer and compliance with any laws or regulations pertaining to said transfer.

4.     Withholding of Taxes. Notwithstanding any contrary provision of this Award Agreement, no certificate representing the Shares will be issued to Participant, unless and until satisfactory arrangements (as determined by the Administrator) will have been made by Participant with respect to the payment of income, employment, social insurance, payroll and other taxes which the Company determines must be withheld with respect to such Shares. Prior to vesting and/or settlement of the Restricted Stock Units, Participant will pay or make adequate arrangements satisfactory to the Company and/or Participant’s employer (the “Employer”) to satisfy all withholding and payment obligations of the Company and/or the Employer. In this regard, Participant authorizes the Company and/or the Employer to withhold all applicable tax withholding obligations legally payable by Participant from his or her wages or other cash compensation paid to Participant by the Company and/or the Employer or from proceeds of the sale of Shares. Alternatively, or in addition, if permissible under applicable local law, the Administrator, in its sole discretion and pursuant to such procedures as it may specify from time to time, may permit or require Participant to satisfy such tax withholding obligation, in whole or in part (without limitation) by (a) paying cash, (b) electing to have the Company withhold otherwise deliverable Shares having a Fair Market Value equal to the minimum amount required to be withheld, (c) delivering to the Company already vested and owned Shares having a Fair Market Value equal to the amount required to be withheld, or (d) selling a sufficient number of such Shares otherwise deliverable to Participant through such means as the Company may determine in its sole discretion (whether through a broker or otherwise) equal to the amount required to be withheld. To the extent determined appropriate by the Company in its discretion, it will have the right (but not the obligation) to satisfy any tax withholding obligations by reducing the number of Shares otherwise deliverable to Participant and, until determined otherwise by the Company, this will be the method by which such tax withholding obligations are satisfied. If Participant fails to make satisfactory arrangements for the payment of any required tax withholding obligations hereunder at the time any applicable Restricted Stock Units otherwise are scheduled to vest pursuant to Sections 3 or 4 or tax withholding obligations related to Restricted Stock Units otherwise are due, Participant will permanently forfeit such Restricted Stock Units and any right to receive Shares thereunder and the Restricted Stock Units will be returned to the Company at no cost to the Company.

5.     Rights as Stockholder. Neither Participant nor any person claiming under or through Participant will have any of the rights or privileges of a stockholder of the Company in respect of any Shares deliverable hereunder unless and until certificates representing such Shares will have been issued, recorded on the records of the Company or its transfer agents or registrars, and delivered to Participant. After such issuance, recordation and delivery, Participant will have all the rights of a stockholder of the Company with respect to voting such Shares and receipt of dividends and distributions on such Shares.

6.     No Guarantee of Continued Service. PARTICIPANT ACKNOWLEDGES AND AGREES THAT THIS AWARD AGREEMENT AND THE TRANSACTIONS CONTEMPLATED HEREUNDER DO NOT CONSTITUTE AN EXPRESS OR IMPLIED PROMISE OF CONTINUED ENGAGEMENT AS A SERVICE PROVIDER FOR ANY PERIOD, OR AT ALL, AND WILL NOT INTERFERE IN ANY WAY WITH PARTICIPANT’S RIGHT OR THE RIGHT OF THE COMPANY (OR THE PARENT OR SUBSIDIARY EMPLOYING OR RETAINING PARTICIPANT) TO TERMINATE PARTICIPANT’S RELATIONSHIP AS A SERVICE PROVIDER AT ANY TIME, WITH OR WITHOUT CAUSE.

7.     Address for Notices. Any notice to be given to the Company under the terms of this Award Agreement will be addressed to the Company at BioCardia, Inc., 125 Shoreway Road, Suite B, San Carlos, California 94070, or at such other address as the Company may hereafter designate in writing.

8.     Grant is Not Transferable. Except to the limited extent provided in Section 6, this grant and the rights and privileges conferred hereby will not be transferred, assigned, pledged or hypothecated in any way (whether by operation of law or otherwise) and will not be subject to sale under execution, attachment or similar process. Upon any attempt to transfer, assign, pledge, hypothecate or otherwise dispose of this grant, or any right or privilege conferred hereby, or upon any attempted sale under any execution, attachment or similar process, this grant and the rights and privileges conferred hereby immediately will become null and void.

9.     Binding Agreement. Subject to the limitation on the transferability of this grant contained herein, this Award Agreement will be binding upon and inure to the benefit of the heirs, legatees, legal representatives, successors and assigns of the parties hereto.

10.     Additional Conditions to Issuance of Stock. If at any time the Company will determine, in its discretion, that the listing, registration, qualification or rule compliance of the Shares upon any securities exchange or under any state, federal or foreign law, the tax code and related regulations or the consent or approval of any governmental regulatory authority is necessary or desirable as a condition to the issuance of Shares to Participant (or his or her estate) hereunder, such issuance will not occur unless and until such listing, registration, qualification, rule compliance, consent or approval will have been completed, effected or obtained free of any conditions not acceptable to the Company. Where the Company determines that the delivery of the payment of any Shares will violate federal securities laws or other applicable laws, the Company will defer delivery until the earliest date at which the Company reasonably anticipates that the delivery of Shares will no longer cause such violation. The Company will make all reasonable efforts to meet the requirements of any such state, federal or foreign law or securities exchange and to obtain any such consent or approval of any such governmental authority or securities exchange.

11.     Plan Governs. This Award Agreement is subject to all terms and provisions of the Plan. In the event of a conflict between one or more provisions of this Award Agreement and one or more provisions of the Plan, the provisions of the Plan will govern. Capitalized terms used and not defined in this Award Agreement will have the meaning set forth in the Plan.

12.     Administrator Authority. The Administrator will have the power to interpret the Plan and this Award Agreement and to adopt such rules for the administration, interpretation and application of the Plan as are consistent therewith and to interpret or revoke any such rules. All actions taken and all interpretations and determinations made by the Administrator in good faith will be final and binding upon Participant, the Company and all other interested persons. No member of the Administrator will be personally liable for any action, determination or interpretation made in good faith with respect to the Plan or this Award Agreement.

13.     Electronic Delivery. The Company may, in its sole discretion, decide to deliver any documents related to Restricted Stock Units awarded under the Plan or future Restricted Stock Units that may be awarded under the Plan by electronic means or request Participant’s consent to participate in the Plan by electronic means. Participant hereby consents to receive such documents by electronic delivery and agrees to participate in the Plan through any on-line or electronic system established and maintained by the Company or a third party designated by the Company.

14.     Captions. Captions provided herein are for convenience only and are not to serve as a basis for interpretation or construction of this Award Agreement.

15.     Agreement Severable. In the event that any provision in this Award Agreement will be held invalid or unenforceable, such provision will be severable from, and such invalidity or unenforceability will not be construed to have any effect on, the remaining provisions of this Award Agreement.

16.     Modifications to the Award Agreement. This Award Agreement constitutes the entire understanding of the parties on the subjects covered. Participant expressly warrants that he or she is not accepting this Award Agreement in reliance on any promises, representations, or inducements other than those contained herein. Modifications to this Award Agreement or the Plan can be made only in an express written contract executed by a duly authorized officer of the Company. Notwithstanding anything to the contrary in the Plan or this Award Agreement, the Company reserves the right to revise this Award Agreement as it deems necessary or advisable, in its sole discretion and without the consent of Participant, to comply with Section 409A or to otherwise avoid imposition of any additional tax or income recognition under Section 409A in connection to this Award of Restricted Stock Units.

17.     Amendment, Suspension or Termination of the Plan. By accepting this Award, Participant expressly warrants that he or she has received an Award of Restricted Stock Units under the Plan, and has received, read and understood a description of the Plan. Participant understands that the Plan is discretionary in nature and may be amended, suspended or terminated by the Company at any time.

18.     Governing Law. This Award Agreement will be governed by the laws of California, without giving effect to the conflict of law principles thereof. For purposes of litigating any dispute that arises under this Award of Restricted Stock Units or this Award Agreement, the parties hereby submit to and consent to the jurisdiction of the State of California, and agree that such litigation will be conducted in the courts of San Mateo County, California, or the federal courts for the United States for the Northern District of California, and no other courts, where this Award of Restricted Stock Units is made and/or to be performed.