--- a/devtools/client/inspector/markup/markup.js
+++ b/devtools/client/inspector/markup/markup.js
@@ -413,30 +413,32 @@ MarkupView.prototype = {
    *
    * @param  {NodeFront} nodeFront
    *         The node to show the highlighter for
    * @return {Promise} Resolves when the highlighter for this nodeFront is
    *         shown, taking into account that there could already be highlighter
    *         requests queued up
    */
   _showBoxModel: function (nodeFront) {
-    return this.toolbox.highlighterUtils.highlightNodeFront(nodeFront);
+    return this.toolbox.highlighterUtils.highlightNodeFront(nodeFront)
+      .catch(this._handleRejectionIfNotDestroyed);
   },
 
   /**
    * Hide the box model highlighter on a given node front
    *
    * @param  {Boolean} forceHide
    *         See toolbox-highlighter-utils/unhighlight
    * @return {Promise} Resolves when the highlighter for this nodeFront is
    *         hidden, taking into account that there could already be highlighter
    *         requests queued up
    */
   _hideBoxModel: function (forceHide) {
-    return this.toolbox.highlighterUtils.unhighlight(forceHide);
+    return this.toolbox.highlighterUtils.unhighlight(forceHide)
+      .catch(this._handleRejectionIfNotDestroyed);
   },
 
   _briefBoxModelTimer: null,
 
   _clearBriefBoxModelTimer: function () {
     if (this._briefBoxModelTimer) {
       clearTimeout(this._briefBoxModelTimer);
       this._briefBoxModelPromise.resolve();