diff --git a/Misc/NEWS.d/next/C API/2020-03-13-16-44-23.bpo-35370.sXRA-r.rst b/Misc/NEWS.d/next/C API/2020-03-13-16-44-23.bpo-35370.sXRA-r.rst
new file mode 100644
index 00000000000..d3f1d293b69
--- /dev/null
+++ b/Misc/NEWS.d/next/C API/2020-03-13-16-44-23.bpo-35370.sXRA-r.rst	
@@ -0,0 +1,2 @@
+If :c:func:`PySys_Audit` fails in :c:func:`PyEval_SetProfile` or
+:c:func:`PyEval_SetTrace`, log the error as an unraisable exception.
diff --git a/Python/ceval.c b/Python/ceval.c
index fc4f718de28..b359fb07984 100644
--- a/Python/ceval.c
+++ b/Python/ceval.c
@@ -4620,7 +4620,10 @@ void
 PyEval_SetProfile(Py_tracefunc func, PyObject *arg)
 {
     PyThreadState *tstate = _PyThreadState_GET();
-    (void)_PyEval_SetProfile(tstate, func, arg);
+    if (_PyEval_SetProfile(tstate, func, arg) < 0) {
+        /* Log PySys_Audit() error */
+        _PyErr_WriteUnraisableMsg("in PyEval_SetProfile", NULL);
+    }
 }
 
 int
@@ -4661,7 +4664,10 @@ void
 PyEval_SetTrace(Py_tracefunc func, PyObject *arg)
 {
     PyThreadState *tstate = _PyThreadState_GET();
-    (void)_PyEval_SetTrace(tstate, func, arg);
+    if (_PyEval_SetTrace(tstate, func, arg) < 0) {
+        /* Log PySys_Audit() error */
+        _PyErr_WriteUnraisableMsg("in PyEval_SetTrace", NULL);
+    }
 }