Unfortunately there is no perfect size as its all responsive and there are so many screen size to do it for its close to impossible to determine the perfect size..
Having said that, I'm still able to provide to you certain guidelines to ensure you have the almost perfect header each time.
Here is an example which I have on my account.
The main idea for having a almost perfect cover image is to understand that all the designs are basically centred. In this case this image size is set to 2048px x 512px with the middle portion is about 350 px - 400 px where you name , reputation and other information would be.
To actually calculate and start designing. This is the basic pixel for you to begin your designs. By the way .. the basic height is actually less then 512 px however by placing it at 512 px in height you will be sure that your screen will always be filled.
Here are a few free cover images taken from Unsplash.com
Free Photo by Brady Bellini on Unsplash
Photo by rawpixel.com on Unsplash
Photo by nikita velikanin on Unsplash
Hope you have fun designing your own banners for your steem account. A quick way to design is by using canva.com which is super convenient to use and can get you started almost immediately.
Best way is to play around and find which design works well for your profile. Cheers.
Even i have been looking for the answer of this question for some time and i decided to review the page source. In the debugger I inspected the cover photo and in the menu selected layout to see the exact size for the photo.
And that's how I got my result of 1354 x 155 pixels. Hope this helps and soon you get a nice cover shot too! Cheers ! Keep Steeming