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<span id="hiw06302021ex321.htm"></span><!DOCTYPE html PUBLIC "-//W3C//DTD HTML 4.01 Transitional//EN" "http://www.w3.org/TR/html4/loose.dtd"><html lang="en-US"><head> <!-- Document created using Wdesk --> <!-- Copyright 2021 Workiva --> <title>Form 10-Q filed by on 2021-07-27</title></head><body><div id="ib625987bd4f444e389b9221488dc7158_1"></div><div style="min-height:42.75pt;width:100%"><div><font><br></font></div></div><div style="text-align:right"><font style="color:#000000;font-family:'Times New Roman',sans-serif;font-size:10pt;font-weight:700;line-height:120%">Exhibit 32.1</font></div><div><font><br></font></div><div style="text-align:center"><font style="color:#000000;font-family:'Times New Roman',sans-serif;font-size:10pt;font-weight:700;line-height:120%">CERTIFICATION PURSUANT TO SECTION 906</font></div><div style="text-align:center"><font style="color:#000000;font-family:'Times New Roman',sans-serif;font-size:10pt;font-weight:700;line-height:120%">OF THE SARBANES-OXLEY ACT</font></div><div><font><br></font></div><div style="text-align:justify;text-indent:18pt"><font style="color:#000000;font-family:'Times New Roman',sans-serif;font-size:10pt;font-weight:400;line-height:120%">In connection with the Quarterly Report of Highwoods Properties, Inc. (the “Company”) on Form 10-Q for the period ended June 30, 2021 as filed with the Securities and Exchange Commission on the date hereof (the “Report”), I, Theodore J. Klinck, President and Chief Executive Officer of the Company, certify, pursuant to 18 U.S.C. § 1350, as adopted pursuant to § 906 of the Sarbanes-Oxley Act of 2002, that:</font></div><div style="text-align:justify;text-indent:18pt"><font><br></font></div><div style="padding-left:36pt;text-align:justify;text-indent:-18pt"><font style="color:#000000;font-family:'Times New Roman',sans-serif;font-size:10pt;font-weight:400;line-height:120%">1)</font><font style="color:#000000;font-family:'Times New Roman',sans-serif;font-size:10pt;font-weight:400;line-height:120%;padding-left:9.67pt">The Report fully complies with the requirements of Section 13(a) or 15(d) of the Securities Exchange Act of 1934, as amended; and</font></div><div style="padding-left:36pt;text-align:justify;text-indent:-18pt"><font style="color:#000000;font-family:'Times New Roman',sans-serif;font-size:10pt;font-weight:400;line-height:120%">2)</font><font style="color:#000000;font-family:'Times New Roman',sans-serif;font-size:10pt;font-weight:400;line-height:120%;padding-left:9.67pt">The information contained in the Report fairly presents, in all material respects, the financial condition and results of operations of the Company.</font></div><div style="text-align:justify"><font style="color:#000000;font-family:'Times New Roman',sans-serif;font-size:10pt;font-weight:400;line-height:120%"> </font></div><div style="margin-top:5pt"><table style="border-collapse:collapse;display:inline-table;margin-bottom:5pt;vertical-align:text-bottom;width:249.75pt"><tr><td style="width:1.0pt"></td><td style="width:247.75pt"></td><td style="width:1.0pt"></td></tr><tr style="height:14pt"><td colspan="3" style="padding:2px 1pt;text-align:left;vertical-align:bottom"><font style="color:#000000;font-family:'Times New Roman',sans-serif;font-size:10pt;font-weight:400;line-height:100%">/s/ Theodore J. Klinck</font></td></tr><tr style="height:23pt"><td colspan="3" style="border-top:2pt solid #000000;padding:2px 1pt;text-align:left;vertical-align:bottom"><font style="color:#000000;font-family:'Times New Roman',sans-serif;font-size:10pt;font-weight:400;line-height:100%">Theodore J. Klinck<br>President and Chief Executive Officer</font></td></tr><tr style="height:14pt"><td colspan="3" style="padding:2px 1pt;text-align:left;vertical-align:top"><font style="color:#000000;font-family:'Times New Roman',sans-serif;font-size:10pt;font-weight:400;line-height:100%">July 27, 2021</font></td></tr></table></div><div style="height:42.75pt;position:relative;width:100%"><div style="bottom:0;position:absolute;width:100%"><div style="text-align:center"><font><br></font></div></div></div></body></html>