The Southampton rockers play their biggest Glasgow show so far on Tuesday, headlining the O2 ABC.
But after supporting the Chilis in various giant arenas in America, the trio believe they can handle anything.
"We were going from a couple of hundred people at our own shows in America to 15,000 the next night," says bassist Emma Richardson.
"We hadn't played to that many people before and we had to trust the equipment and the PA as we couldn't hear ourselves.
"It was a voyage of discovery, but it went really well. The crowd really responded well. We didn't know what Chilis fans would be like to us, but they were actually cheering a lot and we got a standing ovation in Denver, which was nice."
And the headliners were a pleasure to deal with, according to Emma.
"Chad and Flea came over and welcomed us on tour," she adds. "They were really nice, and it was a great tour to be on, as all the crew were brilliant.
"We watched them every night, and it was great to see that sort of production with the lighting and the screens and everything."
Band Of Skulls are clearly in demand for support slots, given that they've been hand-picked to play alongside Muse on their European arena tour next year.
But the Skulls – Emma, Matt Hayward and Russell Marsden – who have been playing together in bands for nearly a decade, are also doing well on their own.
Second album Sweet Sour brought their swaggering blues rock to a bigger audience than before, and Emma believes it was an album written to be played live.
"We definitely wanted Sweet Sour to be a live record, it really suits our writing," she says. "Getting to play it now and getting such a reaction is testament to the fact that it really works.
"Some of the quieter tracks on there have surprised me though. It can be more exciting sometimes to figure out how to make that kind of song work in a bigger room.
"It's good to be able to bring it down and quieten things in a loud rock set.
"We always try and write beyond our ability, and then get better so we can actually perform the song live."
The band honed their craft with years of gigging, something Emma feels was a great boost to them.
She's also delighted they didn't have to suffer the pressure that goes with being signed to a big label early in their career.
"It would have been a false presentation of our band if we'd got signed up to a major label," she explains.
"That's quite scary for a band because you get all the press and all the hype, and then you've got to pull it out the bag.
"I'm glad we came out of it after about 10 years of playing together and about five years in Band of Skulls as I think you can discover more about yourself as a group by gigging lots before making an album."
The band's success and style have led to comparisons, with their blues influences, and they are often mentioned alongside the Black Keys and Jack White.
Emma is happy to be spoken of in the same breath as those acts, although she doesn't think they're actually alike.
"I don't mind it, people have got to connect you to something to explain you to other people," she says.
"I don't think we're actually like those bands. We do what we do. It's a compliment though, as we like those bands, but we're not trying to ape them."
And the Skulls can't wait to get to Glasgow.
"We've played Glasgow quite a few times, and it's usually a good gig and then a wild night out drinking afterwards," says Emma, with a laugh.
"It's always great fun. We've played King Tut's a few times and every time we go up there it's a good one."
l Band of Skulls, O2 ABC, Tuesday, 7pm, £15. Tickets avaiiable from gigsinscotland