diff --git a/packages/base-manager/src/utils.ts b/packages/base-manager/src/utils.ts
index 0e0c7f59ba..c49f3fc369 100644
--- a/packages/base-manager/src/utils.ts
+++ b/packages/base-manager/src/utils.ts
@@ -298,3 +298,22 @@ export function bufferToBase64(buffer: ArrayBuffer): string {
 export function base64ToBuffer(base64: string): ArrayBuffer {
   return toByteArray(base64).buffer;
 }
+
+/**
+ * Map a function onto a list in batches, resolving each batch of returned
+ * promises before moving to the next batch.
+ */
+export async function mapBatch<T, U>(
+  list: T[],
+  step: number,
+  fn: (value: T, index: number, array: T[]) => Promise<U> | U,
+  thisArg?: any
+): Promise<U[]> {
+  const results = [];
+  for (let i = 0; i < list.length; i += step) {
+    results.push(
+      ...(await Promise.all(list.slice(i, i + step).map(fn, thisArg)))
+    );
+  }
+  return results;
+}
diff --git a/packages/jupyterlab-manager/src/manager.ts b/packages/jupyterlab-manager/src/manager.ts
index c1b306339a..aaa363c63f 100644
--- a/packages/jupyterlab-manager/src/manager.ts
+++ b/packages/jupyterlab-manager/src/manager.ts
@@ -19,7 +19,8 @@ import {
 import {
   ManagerBase,
   serialize_state,
-  IStateOptions
+  IStateOptions,
+  mapBatch
 } from '@jupyter-widgets/base-manager';
 
 import { IDisposable } from '@lumino/disposable';
@@ -144,9 +145,14 @@ export abstract class LabWidgetManager extends ManagerBase<Widget>
     }
     const comm_ids = await this._get_comm_info();
 
-    // For each comm id that we do not know about, create the comm, and request the state.
-    const widgets_info = await Promise.all(
-      Object.keys(comm_ids).map(async comm_id => {
+    // For each comm id that we do not know about, create the comm, and
+    // request the state. We must do this in batches to make sure we do not
+    // exceed the ZMQ high water mark limiting messages from the kernel. See
+    // https://github.com/voila-dashboards/voila/issues/534 for more details.
+    const widgets_info = await mapBatch(
+      Object.keys(comm_ids),
+      100,
+      async comm_id => {
         try {
           await this.get_model(comm_id);
           // If we successfully get the model, do no more.
@@ -192,7 +198,7 @@ export abstract class LabWidgetManager extends ManagerBase<Widget>
 
           return info.promise;
         }
-      })
+      }
     );
 
     // We put in a synchronization barrier here so that we don't have to
diff --git a/widgetsnbextension/src/manager.js b/widgetsnbextension/src/manager.js
index 78dd66eb49..4d1aef0e76 100644
--- a/widgetsnbextension/src/manager.js
+++ b/widgetsnbextension/src/manager.js
@@ -3,7 +3,7 @@
 'use strict';
 
 var base = require('@jupyter-widgets/base');
-var ManagerBase = require('@jupyter-widgets/base-manager').ManagerBase;
+var baseManager = require('@jupyter-widgets/base-manager');
 var widgets = require('@jupyter-widgets/controls');
 var outputWidgets = require('./widget_output');
 var saveState = require('./save_state');
@@ -74,7 +74,7 @@ function new_comm(
 // WidgetManager class
 //--------------------------------------------------------------------
 
-export class WidgetManager extends ManagerBase {
+export class WidgetManager extends baseManager.ManagerBase {
   constructor(comm_manager, notebook) {
     super();
     // Managers are stored in *reverse* order, so that _managers[0] is the most recent.
@@ -111,34 +111,32 @@ export class WidgetManager extends ManagerBase {
       // for the responses (2).
       return Promise.all(comm_promises)
         .then(function(comms) {
-          return Promise.all(
-            comms.map(function(comm) {
-              var update_promise = new Promise(function(resolve, reject) {
-                comm.on_msg(function(msg) {
-                  base.put_buffers(
-                    msg.content.data.state,
-                    msg.content.data.buffer_paths,
-                    msg.buffers
-                  );
-                  // A suspected response was received, check to see if
-                  // it's a state update. If so, resolve.
-                  if (msg.content.data.method === 'update') {
-                    resolve({
-                      comm: comm,
-                      msg: msg
-                    });
-                  }
-                });
+          return baseManager.mapBatch(comms, 100, function(comm) {
+            var update_promise = new Promise(function(resolve, reject) {
+              comm.on_msg(function(msg) {
+                base.put_buffers(
+                  msg.content.data.state,
+                  msg.content.data.buffer_paths,
+                  msg.buffers
+                );
+                // A suspected response was received, check to see if
+                // it's a state update. If so, resolve.
+                if (msg.content.data.method === 'update') {
+                  resolve({
+                    comm: comm,
+                    msg: msg
+                  });
+                }
               });
-              comm.send(
-                {
-                  method: 'request_state'
-                },
-                that.callbacks()
-              );
-              return update_promise;
-            })
-          );
+            });
+            comm.send(
+              {
+                method: 'request_state'
+              },
+              that.callbacks()
+            );
+            return update_promise;
+          });
         })
         .then(function(widgets_info) {
           return Promise.all(
@@ -411,7 +409,10 @@ export class WidgetManager extends ManagerBase {
    * Callback handlers for a specific view
    */
   callbacks(view) {
-    var callbacks = ManagerBase.prototype.callbacks.call(this, view);
+    var callbacks = baseManager.ManagerBase.prototype.callbacks.call(
+      this,
+      view
+    );
     if (view && view.options.iopub_callbacks) {
       callbacks.iopub = view.options.iopub_callbacks;
     }