sure.
You need to do a couple of things:
1) Expand.
2) Go to war and take some of their cities, thus reducing their ability to research.. Also, taking their cities may allow you to demand some techs from them in exchange for peace.
War, if you behind in tech, can be painful - you will probably need bombard units. It may seem bad to send archers up against pikes, but if you redline the pikes (for instance), a vet archer can kill a pike.
The other thing is that, on emperor, it can be cheaper to buy a tech than research it, so those outrageous demands may be less than what you would have to spend in actually researching. Especially if you can find a couple of AI's who don't have the tech, if you buy it you might be able to resell it and make some of that money back.
But, on emp and above, it's not that uncommon to be behind the AI.