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**EXHIBIT**** ****12.1**

**CERTIFICATION OF THE PRINCIPAL EXECUTIVE OFFICER**

I, Jan G. van de Winkel, certify that:

        1.     I have reviewed this annual report on Form 20-F of Genmab A/S;

        2.     Based on my knowledge, this report does not contain any untrue statement of a material fact or omit to state a material fact necessary to make the statements made, in light of the circumstances under which such statements were made, not misleading with respect to the period covered by this report;

        3.     Based on my knowledge, the financial statements, and other financial information included in this report, fairly present in all material respects the financial condition, results of operations and cash flows of Genmab A/S as of, and for, the periods presented in this report;

        4.     The other certifying officer of Genmab A/S and I are responsible for establishing and maintaining disclosure controls and procedures (as defined in Exchange Act Rules 13a-15(e) and 15d-15(e)) and internal control over financial reporting (as defined in Exchange Act Rules 13a-15(f) and 15d-15(f)) for Genmab A/S and have:

        (a)   Designed such disclosure controls and procedures, or caused such disclosure controls and procedures to be designed under our supervision, to ensure that material information relating to Genmab A/S, including its consolidated subsidiaries, is made known to us by others within those entities, particularly during the period in which this report is being prepared;

      (b)   Designed such internal control over financial reporting, or caused such internal control over financial reporting to be designed under our supervision, to provide reasonable assurance regarding the reliability of financial reporting and the preparation of financial statements for external purposes in accordance with generally accepted accounting principles;

        (c)   Evaluated the effectiveness of disclosure controls and procedures of Genmab A/S and presented in this report our conclusions about the effectiveness of the disclosure controls and procedures, as of the end of the period covered by this report based on such evaluation; and

        (d)   Disclosed in this report any change in internal control over financial reporting of Genmab A/S that occurred during the period covered by the annual report that has materially affected, or is reasonably likely to materially affect internal control over financial reporting of Genmab A/S.

        5.     The other certifying officer of Genmab A/S and I have disclosed, based on our most recent evaluation of internal control over financial reporting, to the auditors of Genmab A/S and the audit committee of the board of directors of Genmab A/S (or persons performing the equivalent functions):

        (a)   All significant deficiencies and material weaknesses in the design or operation of internal control over financial reporting which are reasonably likely to adversely affect the ability of Genmab A/S to record, process, summarize and report financial information; and

        (b)   Any fraud, whether or not material, that involves management or other employees who have a significant role in the internal control over financial reporting of Genmab A/S.

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| Date: February 16, 2022  | ​ |
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| /s/ Jan G. van de Winkel | ​ |

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AMERICAS/2017215015.2

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