diff --git a/Marlin/src/feature/bedlevel/ubl/ubl_G29.cpp b/Marlin/src/feature/bedlevel/ubl/ubl_G29.cpp
index 6f5187cc9f..ed4363acbc 100644
--- a/Marlin/src/feature/bedlevel/ubl/ubl_G29.cpp
+++ b/Marlin/src/feature/bedlevel/ubl/ubl_G29.cpp
@@ -786,14 +786,18 @@ void unified_bed_leveling::shift_mesh_height() {
         }
       #endif
 
-      best = do_furthest
+      #ifndef HUGE_VALF
+        #define HUGE_VALF (10e100F)
+      #endif
+
+      best = do_furthest // Points with valid data or HUGE_VALF are skipped
         ? find_furthest_invalid_mesh_point()
         : find_closest_mesh_point_of_type(INVALID, nearby, true);
 
       if (best.pos.x >= 0) {    // mesh point found and is reachable by probe
         TERN_(EXTENSIBLE_UI, ExtUI::onMeshUpdate(best.pos, ExtUI::G29_POINT_START));
         const float measured_z = probe.probe_at_point(best.meshpos(), stow_probe ? PROBE_PT_STOW : PROBE_PT_RAISE, param.V_verbosity);
-        z_values[best.pos.x][best.pos.y] = measured_z;
+        z_values[best.pos.x][best.pos.y] = isnan(measured_z) ? HUGE_VALF : measured_z;  // Mark invalid point already probed with HUGE_VALF to omit it in the next loop
         #if ENABLED(EXTENSIBLE_UI)
           ExtUI::onMeshUpdate(best.pos, ExtUI::G29_POINT_FINISH);
           ExtUI::onMeshUpdate(best.pos, measured_z);
@@ -803,6 +807,8 @@ void unified_bed_leveling::shift_mesh_height() {
 
     } while (best.pos.x >= 0 && --count);
 
+    GRID_LOOP(x, y) if (z_values[x][y] == HUGE_VALF) z_values[x][y] = NAN; // Restore NAN for HUGE_VALF marks
+
     TERN_(EXTENSIBLE_UI, ExtUI::onMeshUpdate(best.pos, ExtUI::G29_FINISH));
 
     // Release UI during stow to allow for PAUSE_BEFORE_DEPLOY_STOW