Go look at the circuit breaker or fuses feeding the present cook-top and see what size they are.

It is very unlikely they will be oversize wiring on the circuit, so if you need 50 amps you are probably going to have to run a new branch circuit.

If the wiring is in an area that is unfinished and has easy access it will not be very expensive.

It you have a finished basement it is likely going to require wall damage and ceiling damage, or the line could be put in conduit on the outside of the house (ugly but sometimes cheaper than tearing up a lot of wall and ceiling).

The circuit breaker box showed 2 "switches" for cooktop with "30" on one switch. The house is 25 years old. What is a "branch circuit", and how would you "add it on" to my existing setup?

gilbert 2007 wrote- What is a "branch circuit", and how would you "add it on" to my existing setup?

"Branch circuit" is the technical description of the circuit breaker, wiring and receptacle that your cooktop plugs in to.

I would "add it on" by going to my shop, picking up the needed tools and material and installing same. On the other hand, you should probably call an electrician. He or she will do something along those lines, and take your money in exchange.

30 means 30 amps for your current stove.

A 'branch' circuit is a new circuit from the main (trunk) panel to your new stove.

If you have a 30 amp circuit for an existing cook top, my guess is that you also have another 30 amp circuit for a built-in oven. Neither of these will suffice for what you want to do.

If your new cook top calls for a 50 amp CIRCUIT, that is what you will have to have installed.

If the new cook top is actually rated 50 amps, then it will require a 60 amp circuit.

Either way, it will require that a new cable be fished from (probably) the main panel, or (possibly) a subpanel, to the cook top location. It can't be safely connected to your existing wirring.

Thanks Davidr. I think the main panel (or at least the one where the current breaker is) is located pretty far away from the kitchen. But there is also one in the garage, which is very close to the kitchen.
1) What are the chances that I could use the subpanel?
2) Is there a limit to what can be run thru the subpanel?
3) If it were limited, can you increase its capacity to run more circuits easily?

"1) What are the chances that I could use the subpanel?"

You have to perform a load calculation on the circuits in the sub-pane; to determine if there is enough capacity available.

The first check would be what is the size of the disconnect in the sub-panel or in the main panel feeding the sub-panel.

"2) Is there a limit to what can be run thru the subpanel?"

The breaker feeding the sub-panel or the main breaker in the sub-panel set the total limit for the panel.
A load calculation determines how much of that limit is 'used.' Adding up the breakers in the panel is NOT a load calculation.

"3) If it were limited, can you increase its capacity to run more circuits easily?"

It depends on if the problem is a full panel or not enough capacity.

Call an electrician and let them give you an estimate.