diff --git a/src/connection-manager/index.ts b/src/connection-manager/index.ts
index 65de6efd49..39f36be006 100644
--- a/src/connection-manager/index.ts
+++ b/src/connection-manager/index.ts
@@ -254,10 +254,16 @@ export class DefaultConnectionManager extends EventEmitter<ConnectionManagerEven
    */
   async _close () {
     // Close all connections we're tracking
-    const tasks = []
+    const tasks: Array<Promise<void>> = []
     for (const connectionList of this.connections.values()) {
       for (const connection of connectionList) {
-        tasks.push(connection.close())
+        tasks.push((async () => {
+          try {
+            await connection.close()
+          } catch (err) {
+            log.error(err)
+          }
+        })())
       }
     }
 
diff --git a/src/upgrader.ts b/src/upgrader.ts
index 109f2c2e80..27cd729ec9 100644
--- a/src/upgrader.ts
+++ b/src/upgrader.ts
@@ -382,9 +382,11 @@ export class DefaultUpgrader extends EventEmitter<UpgraderEvents> implements Upg
       getStreams: () => muxer != null ? muxer.streams : errConnectionNotMultiplexed(),
       close: async () => {
         await maConn.close()
-        // Ensure remaining streams are aborted
+        // Ensure remaining streams are closed
         if (muxer != null) {
-          muxer.streams.map(stream => stream.abort())
+          await Promise.all(muxer.streams.map(async stream => {
+            await stream.close()
+          }))
         }
       }
     })