There needs to be a consequence, and you need to stick to it.

Make sure you give them a warning first, with a clear indication of the consequences.

Here is an example scenario of how I deal with my kid...

"if you continue to beg me for {item}, not only will you not get the {item}, but you also won't get {ice cream} later. I understand that its upsetting not to get such a cool {item}, and it's okay to feel angry. But it is not okay to carry on about it. Do you want to sit on a bench until you can calm down?"

If the carrying on continues, follow through on your warning, and don't give extra extra extra chances. If she learns you always follow through, she will stop bothering to tantrum over time. While she is having a tantrum, calmly tell her that she won't get her {ice cream} now.

Obviously that will make it worse. Take her to a bench and sit it out until she calms down. (You can catch up to your friends later) Time out is not really about punishment. It's more about regaining composure.

Sometimes, after my kid calms down, we talk about what happened, and I try to think of a way she can earn it back with good behavior.