Figure out which airline would be your best alternative, and call their Elite access number. Explain the situation, and ask them if they’d be willing to give you equivalent status in their program in exchange for your loyalty (usually demonstrated by a destroyed card from the competing program). It works about 60% of the time, in my experience.
From then on, you only fly Continental to use up your miles.
Tech Broiler
Off The Broiler 
Figure out which airline would be your best alternative, and call their Elite access number. Explain the situation, and ask them if they’d be willing to give you equivalent status in their program in exchange for your loyalty (usually demonstrated by a destroyed card from the competing program). It works about 60% of the time, in my experience.
From then on, you only fly Continental to use up your miles.