diff --git a/tests/auto/qfontmetrics/tst_qfontmetrics.cpp b/tests/auto/qfontmetrics/tst_qfontmetrics.cpp
index 1df194d020..982cfc11d9 100644
--- a/tests/auto/qfontmetrics/tst_qfontmetrics.cpp
+++ b/tests/auto/qfontmetrics/tst_qfontmetrics.cpp
@@ -277,12 +277,20 @@ void tst_QFontMetrics::inFontUcs4()
     {
         QFontMetrics fm(font);
 
+#ifdef Q_WS_QPA
+        QEXPECT_FAIL("", "QTBUG-20759 fails for qpa", Continue);
+#endif
+
         QVERIFY(fm.inFontUcs4(0x1D7FF));
     }
 
     {
         QFontMetricsF fm(font);
 
+#ifdef Q_WS_QPA
+        QEXPECT_FAIL("", "QTBUG-20759 fails for qpa", Continue);
+#endif
+
         QVERIFY(fm.inFontUcs4(0x1D7FF));
     }
 
@@ -303,6 +311,11 @@ void tst_QFontMetrics::lineWidth()
     const QFontMetrics bigFontMetrics(bigFont);
 
     QVERIFY(smallFontMetrics.lineWidth() >= 1);
+
+#ifdef Q_WS_QPA
+    QEXPECT_FAIL("", "QTBUG-20759 fails for qpa", Continue);
+#endif
+
     QVERIFY(smallFontMetrics.lineWidth() < bigFontMetrics.lineWidth());
 }