diff --git a/test/test_networking.py b/test/test_networking.py
index 926dc97e97..92fbdc97d9 100644
--- a/test/test_networking.py
+++ b/test/test_networking.py
@@ -61,7 +61,7 @@ from yt_dlp.networking.impersonate import (
     ImpersonateRequestHandler,
     ImpersonateTarget,
 )
-from yt_dlp.utils import YoutubeDLError
+from yt_dlp.utils import YoutubeDLError, traverse_obj
 from yt_dlp.utils._utils import _YDLLogger as FakeLogger
 from yt_dlp.utils.networking import HTTPHeaderDict, std_headers
 
@@ -1762,6 +1762,7 @@ class TestYoutubeDLNetworking:
             'compat_opts': ['no-certifi'],
             'nocheckcertificate': True,
             'legacyserverconnect': True,
+            'proxy_nocheckcertificate': True,
         }) as ydl:
             rh = self.build_handler(ydl)
             assert rh.headers.get('test') == 'testtest'
@@ -1773,6 +1774,7 @@ class TestYoutubeDLNetworking:
             assert rh.prefer_system_certs is True
             assert rh.verify is False
             assert rh.legacy_ssl_support is True
+            assert rh.proxy_verify is False
 
     @pytest.mark.parametrize('ydl_params', [
         {'client_certificate': 'fakecert.crt'},
@@ -1785,6 +1787,22 @@ class TestYoutubeDLNetworking:
             rh = self.build_handler(ydl)
             assert rh._client_cert == ydl_params  # XXX: Too bound to implementation
 
+    @pytest.mark.parametrize('client_cert', [
+        {'client_certificate': 'fakecert.crt'},
+        {'client_certificate': 'fakecert.crt', 'client_certificate_key': 'fakekey.key'},
+        {'client_certificate': 'fakecert.crt', 'client_certificate_key': 'fakekey.key', 'client_certificate_password': 'foobar'},
+        {'client_certificate_key': 'fakekey.key', 'client_certificate_password': 'foobar'},
+    ])
+    def test_proxy_client_certificate(self, client_cert):
+        ydl_params = traverse_obj(client_cert, {
+            'proxy_client_certificate': 'client_certificate',
+            'proxy_client_certificate_key': 'client_certificate_key',
+            'proxy_client_certificate_password': 'client_certificate_password',
+        })
+        with FakeYDL(ydl_params) as ydl:
+            rh = self.build_handler(ydl)
+            assert rh._proxy_client_cert == client_cert
+
     def test_urllib_file_urls(self):
         with FakeYDL({'enable_file_urls': False}) as ydl:
             rh = self.build_handler(ydl, UrllibRH)
diff --git a/yt_dlp/YoutubeDL.py b/yt_dlp/YoutubeDL.py
index 9691a1ea7c..ee7880c12b 100644
--- a/yt_dlp/YoutubeDL.py
+++ b/yt_dlp/YoutubeDL.py
@@ -340,10 +340,15 @@ class YoutubeDL:
     legacyserverconnect: Explicitly allow HTTPS connection to servers that do not
                        support RFC 5746 secure renegotiation
     nocheckcertificate:  Do not verify SSL certificates
+    proxy_nocheckcertificate:  Do not verify SSL certificates for HTTPS proxy
     client_certificate:  Path to client certificate file in PEM format. May include the private key
     client_certificate_key:  Path to private key file for client certificate
     client_certificate_password:  Password for client certificate private key, if encrypted.
                         If not provided and the key is encrypted, yt-dlp will ask interactively
+    proxy_client_certificate:  Path to client certificate file in PEM format for HTTPS proxy. May include the private key
+    proxy_client_certificate_key:  Path to private key file for client certificate for HTTPS proxy.
+    proxy_client_certificate_password:  Password for client certificate private key, if encrypted, for HTTPS proxy.
+                        If not provided and the key is encrypted, yt-dlp will ask interactively
     prefer_insecure:   Use HTTP instead of HTTPS to retrieve information.
                        (Only supported by some extractors)
     enable_file_urls:  Enable file:// URLs. This is disabled by default for security reasons.
@@ -4221,6 +4226,7 @@ class YoutubeDL:
                 proxies=proxies,
                 prefer_system_certs='no-certifi' in self.params['compat_opts'],
                 verify=not self.params.get('nocheckcertificate'),
+                proxy_verify=not self.params.get('proxy_nocheckcertificate'),
                 **traverse_obj(self.params, {
                     'verbose': 'debug_printtraffic',
                     'source_address': 'source_address',
@@ -4233,6 +4239,11 @@ class YoutubeDL:
                         'client_certificate_key': 'client_certificate_key',
                         'client_certificate_password': 'client_certificate_password',
                     },
+                    'proxy_client_cert': {
+                        'client_certificate': 'proxy_client_certificate',
+                        'client_certificate_key': 'proxy_client_certificate_key',
+                        'client_certificate_password': 'proxy_client_certificate_password',
+                    },
                 }),
             ))
         director.preferences.update(preferences or [])