Next time you are opening up a can of food, or when buying canned goods, measure the lid, There is a good chance it will be 3" or 4" across. To get that lid ready to be a base for a big miniature, you'll probably just need a hand held can opener.
Then wash the can lid and file down any left over burs of metal if there are any,
You'll have a nice durable metal base for your big minis. Magnet ready too in case you want to be able to swap bases for various rulesets.
This does not generally work with pull ring type cans, so you might have to change your brands if you get the fancy cans.