diff --git a/spec/core/matchers/async/toBeRejectedWithMatchingSpec.js b/spec/core/matchers/async/toBeRejectedWithMatchingSpec.js
new file mode 100644
index 00000000..1805cea2
--- /dev/null
+++ b/spec/core/matchers/async/toBeRejectedWithMatchingSpec.js
@@ -0,0 +1,78 @@
+describe('#toBeRejectedWithMatching', function() {
+  it('passes if the promise is rejected with something matching the predicate', function() {
+    const matcher = privateUnderTest.asyncMatchers.toBeRejectedWithMatching(),
+      actual = Promise.reject(new Error('nope')),
+      predicate = value => value.message === 'nope';
+
+    return matcher.compare(actual, predicate).then(function(result) {
+      expect(result).toEqual(jasmine.objectContaining({ pass: true }));
+    });
+  });
+
+  it('fails if the promise resolves', function() {
+    const matcher = privateUnderTest.asyncMatchers.toBeRejectedWithMatching(),
+      actual = Promise.resolve(),
+      predicate = () => true;
+
+    return matcher.compare(actual, predicate).then(function(result) {
+      expect(result).toEqual(jasmine.objectContaining({ pass: false }));
+    });
+  });
+
+  it('fails if the promise is rejected with something not matching the predicate', function() {
+    const matcher = privateUnderTest.asyncMatchers.toBeRejectedWithMatching(),
+      actual = Promise.reject('A Bad Apple'),
+      predicate = value => value === 'A Good Orange';
+
+    return matcher.compare(actual, predicate).then(function(result) {
+      expect(result).toEqual(
+        jasmine.objectContaining({
+          pass: false,
+          message:
+            'Expected a promise to be rejected matching a predicate, but the predicate returned "false".'
+        })
+      );
+    });
+  });
+
+  it('should build its error correctly when negated', function() {
+    const matcher = privateUnderTest.asyncMatchers.toBeRejectedWithMatching(),
+      actual = Promise.reject(true),
+      predicate = () => true;
+
+    return matcher.compare(actual, predicate).then(function(result) {
+      expect(result).toEqual(
+        jasmine.objectContaining({
+          pass: true,
+          message:
+            'Expected a promise not to be rejected matching a predicate, but the predicate returned "true".'
+        })
+      );
+    });
+  });
+
+  it('fails if actual is not a promise', function() {
+    const matcher = privateUnderTest.asyncMatchers.toBeRejectedWithMatching(),
+      actual = 'not a promise';
+
+    function f() {
+      return matcher.compare(actual);
+    }
+
+    expect(f).toThrowError(
+      'Expected toBeRejectedWithMatching to be called on a promise but was on a string.'
+    );
+  });
+
+  it('fails if predicate is not a function', function() {
+    const matcher = privateUnderTest.asyncMatchers.toBeRejectedWithMatching(),
+      actual = Promise.resolve(),
+      predicate = 'not a function';
+
+    function f() {
+      return matcher.compare(actual, predicate);
+    }
+
+    expect(f).toThrowError(/Predicate is not a Function/);
+  });
+});
diff --git a/src/core/matchers/async/toBeRejectedWithMatching.js b/src/core/matchers/async/toBeRejectedWithMatching.js
new file mode 100644
index 00000000..c27345db
--- /dev/null
+++ b/src/core/matchers/async/toBeRejectedWithMatching.js
@@ -0,0 +1,64 @@
+getJasmineRequireObj().toBeRejectedWithMatching = function(j$) {
+  'use strict';
+
+  const usageError = j$.private.formatErrorMsg(
+    '<toBeRejectedWithMatching>',
+    'expect(function() {<expectation>}).toBeRejectedWithMatching(<Predicate>)'
+  );
+
+  /**
+   * Expect a promise to be rejected with a value matching a predicate.
+   * @function
+   * @async
+   * @name async-matchers#toBeRejectedWithMatching
+   * @since 6.2.0
+   * @param {Function} predicate - A function that takes the rejected promise value as its parameter and returns true if it matches.
+   * @example
+   * await expectAsync(aPromise).toBeRejectedWithMatching((error) => error.message === 'Some error');
+   * @example
+   * return expectAsync(aPromise).toBeRejectedWithMatching((error) => error.message === 'Some error');
+   */
+  return function toBeRejectedWithMatching() {
+    return {
+      compare: function(actualPromise, predicate) {
+        if (!j$.private.isPromiseLike(actualPromise)) {
+          throw new Error(
+            `Expected toBeRejectedWithMatching to be called on a promise but was on a ${typeof actualPromise}.`
+          );
+        }
+
+        if (typeof predicate !== 'function') {
+          throw new Error(usageError('Predicate is not a Function'));
+        }
+
+        function prefix(passed) {
+          return (
+            'Expected a promise ' +
+            (passed ? 'not ' : '') +
+            'to be rejected matching a predicate'
+          );
+        }
+
+        return actualPromise.then(
+          function() {
+            return {
+              pass: false,
+              message: prefix(false) + ', but it was resolved.'
+            };
+          },
+          function(actualValue) {
+            const result = predicate(actualValue);
+            return {
+              pass: Boolean(result),
+              message:
+                prefix(result) +
+                ', but the predicate returned "' +
+                result +
+                '".'
+            };
+          }
+        );
+      }
+    };
+  };
+};
diff --git a/src/core/matchers/requireAsyncMatchers.js b/src/core/matchers/requireAsyncMatchers.js
index b24717db..0794f88e 100644
--- a/src/core/matchers/requireAsyncMatchers.js
+++ b/src/core/matchers/requireAsyncMatchers.js
@@ -7,7 +7,8 @@ getJasmineRequireObj().requireAsyncMatchers = function(jRequire, j$) {
       'toBeRejected',
       'toBeResolvedTo',
       'toBeRejectedWith',
-      'toBeRejectedWithError'
+      'toBeRejectedWithError',
+      'toBeRejectedWithMatching'
     ],
     matchers = {};