Quoted daily ("Work is on a time and materials basis. Rate: $2,000 per day."). Invoices will typically cover a few weeks of work, depending on the tempo of your engagements, your relationship with a customer, etc.
Also, I've harped on this a time or two, but there are people who get $2,000 a day for something which is indistinguishable from web development in terms of activities performed but which is sold as accomplishing business goals ("making lots of money") with incidental reference to programming.
P.S. Charge more for emergency engagements. The business stopping for a day is worth more than $1,000 even if the business is a taco truck. Don't do professional work for taco trucks.
If anything I still think I'm too lenient but this I'm sure will grow as my confidence dealing with clients grows.
You're over-discounting domain knowledge. Anyone can write in code x+y. It might take much deeper knowledge to know that sometimes, it's x-y, and exactly when that is.
You get what you pay for.
Contractor = 2x permanent employee Consultant = 3x Contractor
So $2k a day sounds on the low side to me but perhaps it works if you're talking 4-6 hour days.