diff --git a/psycopg/connection_int.c b/psycopg/connection_int.c
index 0584b390..37001a8b 100644
--- a/psycopg/connection_int.c
+++ b/psycopg/connection_int.c
@@ -1047,7 +1047,7 @@ static cursorObject *
 _conn_get_async_cursor(connectionObject *self) {
     PyObject *py_curs;
 
-    if (!(py_curs = PyWeakref_GetObject(self->async_cursor))) {
+    if (!(py_curs = psyco_weakref_get_object(self->async_cursor))) {
         PyErr_SetString(PyExc_SystemError,
             "got null dereferencing cursor weakref");
         goto error;
diff --git a/psycopg/cursor_type.c b/psycopg/cursor_type.c
index efdeefcc..0bd36f49 100644
--- a/psycopg/cursor_type.c
+++ b/psycopg/cursor_type.c
@@ -779,7 +779,7 @@ curs_fetchone(cursorObject *self, PyObject *dummy)
        successive requests to reallocate it */
     if (self->row >= self->rowcount
         && self->conn->async_cursor
-        && PyWeakref_GetObject(self->conn->async_cursor) == (PyObject*)self)
+        && psyco_weakref_get_object(self->conn->async_cursor) == (PyObject*)self)
         CLEARPGRES(self->pgres);
 
     return res;
@@ -826,7 +826,7 @@ curs_next_named(cursorObject *self)
        successive requests to reallocate it */
     if (self->row >= self->rowcount
         && self->conn->async_cursor
-        && PyWeakref_GetObject(self->conn->async_cursor) == (PyObject*)self)
+        && psyco_weakref_get_object(self->conn->async_cursor) == (PyObject*)self)
         CLEARPGRES(self->pgres);
 
     return res;
@@ -911,7 +911,7 @@ curs_fetchmany(cursorObject *self, PyObject *args, PyObject *kwords)
        successive requests to reallocate it */
     if (self->row >= self->rowcount
         && self->conn->async_cursor
-        && PyWeakref_GetObject(self->conn->async_cursor) == (PyObject*)self)
+        && psyco_weakref_get_object(self->conn->async_cursor) == (PyObject*)self)
         CLEARPGRES(self->pgres);
 
     /* success */
@@ -980,7 +980,7 @@ curs_fetchall(cursorObject *self, PyObject *dummy)
        successive requests to reallocate it */
     if (self->row >= self->rowcount
         && self->conn->async_cursor
-        && PyWeakref_GetObject(self->conn->async_cursor) == (PyObject*)self)
+        && psyco_weakref_get_object(self->conn->async_cursor) == (PyObject*)self)
         CLEARPGRES(self->pgres);
 
     /* success */
diff --git a/psycopg/utils.c b/psycopg/utils.c
index 93f0636c..46070133 100644
--- a/psycopg/utils.c
+++ b/psycopg/utils.c
@@ -441,3 +441,36 @@ psyco_get_decimal_type(void)
 
     return decimalType;
 }
+
+/* Return the object referred by the weak ref as a borrowed pointer.
+ *
+ * Reproduce the semantics of PyWeakref_GetObject(), which was deprecated in
+ * 3.13.
+ *
+ * I know that it would have been better to reproduce the semantics of
+ * PyWeakref_GetRef(), thank you for the suggestion. However this opens a can
+ * of worms in cursor_type.c. Why so? Glad you ask: because there are many
+ * places in that function where we don't check the return value. That stuff is
+ * convoluted and async: I think in case of failure it would fail of internal
+ * error, but it's not been reported doing so.
+ */
+BORROWED PyObject *
+psyco_weakref_get_object(PyObject *ref)
+{
+#if PY_VERSION_HEX >= 0x030d0000
+    PyObject *obj = NULL;
+    int rv;
+
+    if ((rv = PyWeakref_GetRef(ref, &obj)) > 0) {
+        Py_DECREF(obj);  /* make it weak */
+    }
+    else if (rv == 0) {  /* dead ref */
+        obj = Py_None;
+    }
+    /* else it's an error */
+
+    return obj;
+#else
+    return PyWeakref_GetObject(ref);
+#endif
+}
diff --git a/psycopg/utils.h b/psycopg/utils.h
index 5223d3a5..5850291e 100644
--- a/psycopg/utils.h
+++ b/psycopg/utils.h
@@ -59,6 +59,8 @@ HIDDEN RAISES BORROWED PyObject *psyco_set_error(
 
 HIDDEN PyObject *psyco_get_decimal_type(void);
 
+HIDDEN BORROWED PyObject *psyco_weakref_get_object(PyObject *);
+
 HIDDEN PyObject *Bytes_Format(PyObject *format, PyObject *args);