diff --git a/tests/FILEFORMAT b/tests/FILEFORMAT
index e48427224..9fd179e65 100644
--- a/tests/FILEFORMAT
+++ b/tests/FILEFORMAT
@@ -213,6 +213,7 @@ NTLM
 OpenSSL
 socks
 SSL
+SSLpinning
 TLS-SRP
 TrackMemory
 unittest
diff --git a/tests/data/test2034 b/tests/data/test2034
index 92f6085d1..965c9a1b1 100644
--- a/tests/data/test2034
+++ b/tests/data/test2034
@@ -25,6 +25,7 @@ MooMoo
 <client>
 <features>
 SSL
+SSLpinning
 </features>
 <server>
 https Server-localhost-sv.pem
diff --git a/tests/data/test2035 b/tests/data/test2035
index 8591be271..64282fabe 100644
--- a/tests/data/test2035
+++ b/tests/data/test2035
@@ -17,6 +17,7 @@ PEM certificate
 <client>
 <features>
 SSL
+SSLpinning
 </features>
 <server>
 https Server-localhost-sv.pem
diff --git a/tests/runtests.pl b/tests/runtests.pl
index f52678c49..8802c0c98 100755
--- a/tests/runtests.pl
+++ b/tests/runtests.pl
@@ -224,6 +224,8 @@ my $has_axtls;    # built with axTLS
 my $has_winssl;   # built with WinSSL    (Secure Channel aka Schannel)
 my $has_darwinssl;# build with DarwinSSL (Secure Transport)
 
+my $has_sslpinning; # built with a TLS backend that supports pinning
+
 my $has_shared = "unknown";  # built shared
 
 my $resolver;     # string to hold the resolver backend
@@ -2299,10 +2301,12 @@ sub checksystem {
            }
            elsif ($libcurl =~ /openssl/i) {
                $has_openssl=1;
+               $has_sslpinning=1;
                $ssllib="OpenSSL";
            }
            elsif ($libcurl =~ /gnutls/i) {
                $has_gnutls=1;
+               $has_sslpinning=1;
                $ssllib="GnuTLS";
            }
            elsif ($libcurl =~ /nss/i) {
@@ -2758,6 +2762,11 @@ sub singletest {
                     next;
                 }
             }
+            elsif($1 eq "SSLpinning") {
+                if($has_sslpinning) {
+                    next;
+                }
+            }
             elsif($1 eq "OpenSSL") {
                 if($has_openssl) {
                     next;