There wasn't really any situation where this could be of use. Once a code had been broken, especially a code used widely or at high levels like Enigma or the Japanese 'Purple' code, the information gained passively was more useful to intelligence officers than a single one-time advantage gained from sending confusing broadcasts. I'm doubtful that sending coded messages to enemy forces would have any significant operational use, and in the aftermath the enemy would realise that their codes had been compromised and change them. The British went to great lengths to hide the fact that they had broken the enigma code, and throwing it away for a small advantage in a single operation would have been out of the question.

However, both sides made extensive use of code-based misdirection and obfuscation, and false information could be sent over codes which were known to be broken or just unencrypted channels in order to ensure that the enemy read it. The most famous example of this is in the run-up to the battle of Midway. American intelligence analysts were aware that the Japanese were planning a major naval offensive against a target in the Pacific codenamed "AF". The codebreaking station at Pearl Harbour were fairly sure that AF was the codename for Midway but had no conclusive proof, so the base commander was sent a message via secure undersea cable telling him to broadcast a message in the clear (ie unencrypted) saying that the base's water purification system was damaged and requesting fresh water. This was the kind of thing that could be reasonably broadcast unencrypted, and so didn't raise Japanese suspicions. The Americans were then able to decode a Japanese transmission reporting that the AF was short of water - thus confirming beyond all doubt that AF was Midway. The rest, as they say, is history. The British also made use of fake signals as part of Operation Fortitude, the misdirection operation in the run up to D-Day. A fictional army was created in Scotland, intended to mislead the Germans into thinking that Norway was a potential invasion target, and as part of the deceptions, a huge amount of fake radio traffic was simulated. This ultimately had little effect as there's no evidence the Germans were actually listening for these signals, but nonetheless demonstrates the concept!

Both the British and Germans also made use of wireless radios captured from enemy spies to misdirect and confuse their opponents. In the British case, this was mostly done through willing double agents as part of the 'Double Cross' programme. Most agents parachuted directly into Britain were expected by the British, who were aware of their arrival from decrypted Abwehr messages, and picked up shortly after they landed. Others were recruited by the Abwehr and soon after offered their services to the British, while some, such as Elvira Chaudoir, codenamed Bronx, were recruited by the British to try and get recruited by the Abwehr to then become double agents. There was even one triple agent in the mix - Roman Czerniawski, codenamed Brutus. There are other famous names in the mix such as Eddie Chapman and Juan Pujol Garcia. The British used these double agents, who were equipped with wireless radios to contact the Germans, in order to relay false or misleading information back to mainland Europe. Double agents were used extensively to broadcast misinformation in the run-up to D-Day, and Chapman reported the incorrect locations of V-1 attacks, which were consistently falling in South East London, ensuring that the Germans didn't adjust their aim and hit more densely populated areas of the city.

To a much lesser extent, the Germans were also able to broadcast back false information through captured wireless radios, although captured operators were generally made to send messages under duress, or replaced with Abwehr operators who were capable of mimicking a certain operator's 'fist', or unique way of sending morse code. The Germans were able to send coded messages by extracting the poem or book used as a key by means of torture or interrogation, and when the Allies switched to using one-time pads, these were sometimes captured alongside the operator. The main use of captured operators by the Germans was tricking the allies into dropping weapons or agents directly into their hands. The most famous and successful example of this was Operation North Pole, where Dutch wireless operators captured early on in the war were used to trick the British into sending 54 agents and a significant quanity of arms and ammunition straight to the Germans. The Germans successfully used this trick in France as well, although on a much smaller scale. For example, wireless radios belonging to two Canadian SOE agents and Noor Inayat Khan were 'played back' to the British, resulting in the capture of a number of agents and the loss of some supplies.

So in conclusion sending messages directly to an enemy in their own code would have been of little operational use and a surefire way to let them know that you were reading their messages, but both sides made extensive use of wireless radios belonging to captured enemy agents to misdirect and confuse, and sending unencrypted messages when you knew your enemy was listening was also a valid tactic.

For more on Midway and water tanks, see W. J. Holmes, Double-Edged Secrets: U.S. Naval Intelligence Operations in the Pacific during World War II (1979)

For more on Operation North Pole and 'playing back' allied radios, see MRD Foot, SOE in the Low Countries (2001), and SOE in France (1966)

For German double agents see Ben MacIntyre, Double Cross: The True Story of the D-Day Spies (2012)