new file mode 100644
--- /dev/null
+++ b/h3_ssl_reject_handshake.t
@@ -0,0 +1,166 @@
+#!/usr/bin/perl
+
+# (C) Sergey Kandaurov
+# (C) Nginx, Inc.
+
+# Tests for HTTP/3 protocol, ssl_reject_handshake.
+
+###############################################################################
+
+use warnings;
+use strict;
+
+use Test::More;
+
+BEGIN { use FindBin; chdir($FindBin::Bin); }
+
+use lib 'lib';
+use Test::Nginx;
+use Test::Nginx::HTTP3;
+
+###############################################################################
+
+select STDERR; $| = 1;
+select STDOUT; $| = 1;
+
+eval { require Crypt::Misc; die if $Crypt::Misc::VERSION < 0.067; };
+plan(skip_all => 'CryptX version >= 0.067 required') if $@;
+
+my $t = Test::Nginx->new()->has(qw/http http_v3/)
+	->has_daemon('openssl')->plan(7)
+	->write_file_expand('nginx.conf', <<'EOF');
+
+%%TEST_GLOBALS%%
+
+daemon off;
+
+events {
+}
+
+http {
+    %%TEST_GLOBALS_HTTP%%
+
+    add_header X-Name $ssl_server_name;
+
+    server {
+        listen       127.0.0.1:%%PORT_8980_UDP%% quic;
+        server_name  localhost;
+
+        ssl_reject_handshake on;
+    }
+
+    server {
+        listen       127.0.0.1:%%PORT_8980_UDP%% quic;
+        server_name  virtual;
+
+        ssl_certificate localhost.crt;
+        ssl_certificate_key localhost.key;
+    }
+
+    server {
+        listen       127.0.0.1:%%PORT_8982_UDP%% quic;
+        server_name  localhost;
+
+        ssl_certificate localhost.crt;
+        ssl_certificate_key localhost.key;
+    }
+
+    server {
+        listen       127.0.0.1:%%PORT_8982_UDP%% quic;
+        server_name  virtual1;
+    }
+
+    server {
+        listen       127.0.0.1:%%PORT_8982_UDP%% quic;
+        server_name  virtual2;
+
+        ssl_reject_handshake on;
+    }
+}
+
+EOF
+
+$t->write_file('openssl.conf', <<EOF);
+[ req ]
+default_bits = 2048
+encrypt_key = no
+distinguished_name = req_distinguished_name
+[ req_distinguished_name ]
+EOF
+
+my $d = $t->testdir();
+
+foreach my $name ('localhost') {
+	system('openssl req -x509 -new '
+		. "-config $d/openssl.conf -subj /CN=$name/ "
+		. "-out $d/$name.crt -keyout $d/$name.key "
+		. ">>$d/openssl.out 2>&1") == 0
+		or die "Can't create certificate for $name: $!\n";
+}
+
+$t->write_file('index.html', '');
+
+$t->run();
+
+###############################################################################
+
+my $alert = 0x100 + 112; # "unrecognized_name"
+
+SKIP: {
+# OpenSSL < 1.1.1j requires TLSv1.3-capable certificates in the default server
+# See commit "Modify is_tls13_capable() to take account of the servername cb"
+# Additionally, it was seen with OpenSSL 1.1.1k FIPS as found on RHEL 8.1
+
+my $got = bad('default', 8980);
+skip "OpenSSL too old", 3 if $got && $got == 0x100 + 70; # "protocol_version"
+
+# default virtual server rejected
+
+TODO: {
+local $TODO = 'broken send_alert in LibreSSL' if $t->has_module('LibreSSL');
+
+is(bad('default', 8980), $alert, 'default rejected');
+is(bad(undef, 8980), $alert, 'absent sni rejected');
+
+}
+
+like(get('virtual', 8980), qr/virtual/, 'virtual accepted');
+
+}
+
+# non-default server "virtual2" rejected
+
+like(get('default', 8982), qr/default/, 'default accepted');
+like(get(undef, 8982), qr/200/, 'absent sni accepted');
+like(get('virtual1', 8982), qr/virtual1/, 'virtual 1 accepted');
+
+TODO: {
+local $TODO = 'broken send_alert in LibreSSL' if $t->has_module('LibreSSL');
+
+is(bad('virtual2', 8982), $alert, 'virtual 2 rejected');
+
+}
+
+###############################################################################
+
+sub get {
+	my ($sni, $port) = @_;
+	my $s = Test::Nginx::HTTP3->new($port, sni => $sni);
+	my $sid = $s->new_stream({ host => $sni });
+	my $frames = $s->read(all => [{ sid => $sid, fin => 1 }]);
+
+	my ($frame) = grep { $_->{type} eq "HEADERS" } @$frames;
+	return $frame->{headers}->{':status'}
+		. ($frame->{headers}->{'x-name'} || '');
+}
+
+sub bad {
+	my ($sni, $port) = @_;
+	my $s = Test::Nginx::HTTP3->new($port, sni => $sni, probe => 1);
+	my $frames = $s->read(all => [{ type => "CONNECTION_CLOSE" }]);
+
+	my ($frame) = grep { $_->{type} eq "CONNECTION_CLOSE" } @$frames;
+	return $frame->{error};
+}
+
+###############################################################################

--- a/lib/Test/Nginx/HTTP3.pm
+++ b/lib/Test/Nginx/HTTP3.pm
@@ -53,6 +53,7 @@ sub new {
 	$self->init();
 	$self->init_key_schedule();
 	$self->initial();
+	return $self if $extra{probe};
 	$self->handshake() or return;
 
 	# RFC 9204, 4.3.1.  Set Dynamic Table Capacity
@@ -2171,6 +2172,7 @@ sub build_tls_client_hello {
 
 sub build_tlsext_server_name {
 	my ($name) = @_;
+	return '' if !defined $name;
 	my $sname = pack('xn', length($name)) . $name;
 	my $snamelist = pack('n', length($sname)) . $sname;
 	pack('n2', 0, length($snamelist)) . $snamelist;