Anyone have tortoises AND a nice garden?

[Naschkatze]

My DH has two tortoises. Since the weather has been warmer DH lets them out to roam (garden is very secure) but they are eating all the plants!
As we recently moved into a new house and spent a ridiculous amount of money doing the garden from scratch it's very annoying. I should add that the borders have the log roll type edging but they just climb over it.

Any tips from tortoise owners?

My parents tortoise, had her 43 years, also has her own lawn and is frequently hand fed but obsessively gets into the vegetable garden and makes a beeline for the lettuces. To be fair they are grown for her. I've seen my Dad walking down the garden, tortoise in hand with a lettuce leaf hanging out of her mouth.

I would recommend you grow lettuces as a diversion. However as I've said they can be obsessive and very determined in their ultimate goal.