diff --git a/lib/rspec/support/spec/stderr_splitter.rb b/lib/rspec/support/spec/stderr_splitter.rb
index 9caa34cd..44315cec 100644
--- a/lib/rspec/support/spec/stderr_splitter.rb
+++ b/lib/rspec/support/spec/stderr_splitter.rb
@@ -21,6 +21,10 @@ def method_missing(name, *args, &block)
         @orig_stderr.__send__(name, *args, &block)
       end
 
+      def clone
+        StdErrSplitter.new(@orig_stderr.clone)
+      end
+
       def ==(other)
         @orig_stderr == other
       end
diff --git a/spec/rspec/support/spec/stderr_splitter_spec.rb b/spec/rspec/support/spec/stderr_splitter_spec.rb
index 7cb7f6d5..1b1ac0d6 100644
--- a/spec/rspec/support/spec/stderr_splitter_spec.rb
+++ b/spec/rspec/support/spec/stderr_splitter_spec.rb
@@ -95,4 +95,25 @@
     end
   end
 
+  it 'does not reuse the stream when cloned' do
+    expect(splitter.to_io).not_to eq(splitter.clone.to_io)
+  end
+
+  # This is essentially what the `to_stderr_from_any_process` matcher attempts
+  # to do in CaptureStreamToTempfile.
+  it 'is able to restore the stream from a cloned StdErrSplitter', :pending => RSpec::Support::Ruby.jruby? do
+    cloned = $stderr.clone
+    expect($stderr.to_io).not_to be_a(File)
+
+    tempfile = Tempfile.new("foo")
+    begin
+      $stderr.reopen(tempfile)
+      expect($stderr.to_io).to be_a(File)
+    ensure
+      $stderr.reopen(cloned)
+      tempfile.close
+      tempfile.unlink
+    end
+    expect($stderr.to_io).not_to be_a(File)
+  end
 end