most Linux wen host options support ASP but you won't be able to run FrontPage ASP on them or interact with Access or MS SQL databases. They run Chilisoft ASP which can still cut the mustard but it's like working with old spec ASP which, in fact, it is.
Until very recently Chilisoft offered you an ASP option on Linux web hosts but you had to code to ASP 2.0 standard to allow things to work and even then you get the odd curved ball. The latest version is far better but web hosts being what they are means finding one who has bothered to install and configure the latest version of Chilisfot is like picking the winning lotto numbers.
To use 'proper' ASP tends to cost more since you have to go with Windows IIS hosting, but most hosts show lower priced plans for ASP support without Access and/or MS SQL support. Running ASP is the easy bit. Interacting with an underlying database is where the cost hit will be and you often find that entry level Windows IIS for ASP pages will start at around £50 plus VAT (ish) but if you want a database as well the cost soars way, way up. It's a shame really because ASP on its own is all well and good but to take real advantage of it you really have to hook it into a database to get the most out of it.
Anyway, this is a link click here given to me some time ago by Forum Editor that I passed on to some of my tight, sorry, make that poor, students who were unable (AKA unwilling) to pay for top end hosting.
On a personal note I've had good service in the past from 2020 Media click here and if memory serves Areti click here is one of Forum Editors favourites, though I hope I'm forgiven if I'm mistaken. My memory isn't what it used to be...
One & One offer Windows IIS hosting with ASP support as well, but I'm not personally recommending them.