Only Allow Certain Shipping Methods

Is there a way to only allow the customer to choose/view certain shipping methods, say UPS 2nd day or next day? We want to hide or not allow the customer to choose ground and 3day shipping.

No. There's no a way to hide them. To prevent them from showing you would need to delete the shipping methods leaving only the ones you require.

Where would we delete the shipping methods? We are using the UPS live rates, so they are dynamically pulled from UPS.

You can delete the shipping methods from administration > configuration > shipping > shipping methods

We don't have that option because we are using UPS (United Parcel Service) - Beta, so we are receiving all possible shipping methods directly from UPS. We can only delete shipping methods (as you suggested) if we use "shipping by order total" or weight.

I think most customers will choose ground shipping for my site just because it's a lot cheaper. But using the UPS shipping rate calculator, ground shipping is not even a choice. I'm on version 1.20. Help!

Update: the no ground shipping option has been resolved once I changed "UPS Packaging Type" from Express Box to Customer Supplied Package.