An answer kindly was offered on Stackoverflow buy Kuba. For some reason I can't leave comments their yet (just joined) so I'll respond to here. Kuba's suggestion:

Manipulate[number, 
  { {number, 0.3, "Number:"}, 
    ControlType -> InputField, 
    TrackingFunction :> Function[number = Clip[#, {0, 1}]]
  }
]

This unfortunately does not restrict entry in the field live. It even permits entry of non-numerical alpha characters. It's perhaps slightly better than filtering it in the result before application.

@Rohit Namjoshi

Although I am not new to Mathematica, I have only newly joined both the stack overflow Mathematica forum and Wolfram Mathematica forum group. I did wonder about what Wolfram Research prefers, whether it is best to post here (on the Wolfram Research forum), or on stack overflow, and whether posting the same question on both causes confusion. Glad for advice or a link to the official policy.

@Eric Rimbey

I had already thought of squeezing the result using Min and Max, but that is really post-validation and does not integrate well with any live field entry restriction or validation message system.

Seems like there should be a better way to add validation with the InputField itself

Yep. Compare with the FormObject system which does enforce restrictions on submission. This StructuredQuantity approach partially does the job (it doesn't prevent non-numerical keyboard entry into the field though):

"oRefP$kPa" -> <|
"Interpreter" -> Restricted["StructuredQuantity", "Kilopascals", {10., 20.}]
|>

It gives a nice validation warning in red on form submission, with an explanation about the allowed range.