One was stolen from a car parked in Links Parade, Carnoustie, between September 11 and 14, while the second was taken from a car parked in Forfar’s Green Street car park, overnight on September 14/15.
These follow a spate of similar thefts in Dundee and Broughty Ferry in August.
Police Scotland said they were likely stolen to extract the precious metals found inside.
A spokesperson said: “There may also have been other thefts or attempted thefts of this type that we have not been informed of.
“Catalytic converters are valued due to their containing quantities of precious metals such as platinum, palladium and rhodium.
“The process to remove them can only take a couple of minutes, particularly when the person removing it is unconcerned about any damage caused by doing so.
“If you are the owner of newer Honda car, particularly the Jazz, please keep your car as secure as possible and be mindful of anyone you see paying it particular attention.”
Anyone with information about these incidents, or who has been a victim of this type of crime and have not yet informed the police, should telephone 101 or speak to any police officer.
Information can also be given anonymously through CrimeStoppers on 0800 555 111 quoting incident reference number 2808 of September 14.
The owners of high-value and high performance cars are also being urged to be wary of a continuing spate of thefts across the north east area.
Since May, 119 vehicles have been stolen from outside properties in the region, with 19 in Tayside alone.
The break-ins and thefts take place mainly in the late evening, or early morning, when the occupants are in bed and there are fewer members of the public around.
In some instances entry is forced to the property and the car keys have been taken after the suspects obtained them from close to the front door.
However, there have been a number of incidents where those responsible have used a signal amplifying device that picks up the frequency of the car key from outside the front door, allowing the car to be driven away without the property being accessed.
Anyone who witnesses anything suspicious around homes and businesses in their communities should contact police immediately.
In addition, members of the public are asked to consider their own security and take all the necessary precautions to prevent further incidents occurring.
Detective Inspector Karen Muirhead said: “Whenever a housebreaking or vehicle theft occurs, it has a profound impact on the victims.
“Preventing these crimes happening in the first instance is our top priority and the public have a vital role to play in this.
“I would urge all homeowners to consider what their current home security looks like and evaluate if it could be enhanced through the use of measures such as alarms, motion-activated lights and CCTV.
“For those with electric key fobs, please consider buying a faraday box or pouch, which blocks the signal from being detected and amplified to open and start your vehicle. At the very least, please do not leave keys near the door or entryway of your home.
“Following engagement with victims, we have established that many prefer to leave keys and valuables near doors so that in the event their homes are broken into, thieves do not venture further inside the property.
"In our experience, the likelihood of this occurring is extremely rare, with most criminals seeking an easy and quick grab, rather than having to search the entire house.
Anyone with information can contact Police Scotland via 101, or alternatively, make an anonymous report to Crimestoppers on 0800 555 111.