diff --git a/lib/assert.js b/lib/assert.js
index ffe803b05..640e6c4d7 100644
--- a/lib/assert.js
+++ b/lib/assert.js
@@ -166,9 +166,10 @@ function wrapAssertions(callbacks) {
 			};
 
 			if (promise) {
-				const result = promise.then(makeNoop, makeRethrow).then(test);
-				pending(this, result);
-				return result;
+				const intermediate = promise.then(makeNoop, makeRethrow).then(test);
+				pending(this, intermediate);
+				// Don't reject the returned promise, even if the assertion fails.
+				return intermediate.catch(noop);
 			}
 
 			try {
@@ -208,10 +209,10 @@ function wrapAssertions(callbacks) {
 			};
 
 			if (promise) {
-				const result = promise
-					.then(noop, reason => test(makeRethrow(reason)));
-				pending(this, result);
-				return result;
+				const intermediate = promise.then(noop, reason => test(makeRethrow(reason)));
+				pending(this, intermediate);
+				// Don't reject the returned promise, even if the assertion fails.
+				return intermediate.catch(noop);
 			}
 
 			try {