What do you do for customer 24/7 support?

Just wondering what others do for 24/7 support for your customers?

I run a web development company, so design, build and host business websites. Being a small business we do not operate 24/7. I as the business owner would receive email or SMS alerts from our monitoring system of issues, but I may not always be available, and I have Do Not Disturb on my phone during the night. I would think this would be comparable to a lot of small web development companies (probably better, because at least I have monitoring and alerts unlike some).

But customers do expect either 100% uptime, or someone available 24/7 when there is an issue. So I would like to look at what options there are available and wondering what others do.

We use Linode as in my experience the servers are much faster and more reliable than with a standard hosting company that would offer 24/7 support. So we moved away from other hosting companies to Linode some years ago, and the hosting service is much better now, but without the support (software support, Apache/MySQL/CMS's etc).

Having Linode's managed service is too costly for a small business, we have approx. 13 servers (I prefer to have many small servers than one big one!), so the fee would just be way too high for us ($1300 per month), especially when we wont need the support often.

I have found other companies online that do a per server fee also, making them too expensive also.

I guess what I would need is someone who just charges for their time on the support rather than a per server fee whether you use their support or not.

What do others do?

Thanks!