The noise figure is about the active circuit portions only.
Think about what where noise comes from in a passive circuit? Thermal noise only.
Where does thermal noise come from? The resistive component of impedance only. And if it's a 2-port, the transfer parameters of its s-parameter matrix should be ideal (a transmission line) and thus not resistive but reactive, so there should be no added noise from the antenna itself (NF = 0 dB).
But an ideal antenna is: matching 50 ohms and effectively a Thevenin source. So what's the thermal noise? Well, probably tiny but it depends: ~ k x T x BW x R. But...
How does this compare to the noise of an amplifier? Well, without even calculating anything, you have the same thermal noise due to 50 ohms in an amplifier at the input.
But you also have other noise sources because it is tube or semiconductor-based: shot noise, partition noise, avalanche noise, flicker noise, burst noise, generation-recombination noise, etc. Basically: same thermal noise + (maybe a lot) more noise. Ergo, it's the amplifier that matters primarily for NF.
For the antenna, you want to measure s-parameters for knowing the s-parameters to know BW and R seen as the Thevenin, but otherwise that's about it. Well, except that you need an Ant Ranch or Anechoic Chamber, reference antenna and vector network analyzer. Except for that. Which is why you will probably just worry about the amplifiers instead and assume it's just a 50 ohm Thevenin source instead.
The amplifier/gain strip does have a NF to worry about which is http://cp.literature.agilent.com/litweb/pdf/5952-8255E.pdf" . The simplest method is to use a power meter and noise reference source but it's not out-of-the-box as a measurement (hence Agilent's extensive literature collection about NF).
When it comes to RF/uW stuff, always check Agilent's application notes and similar literature
http://www.home.agilent.com/agilent/application.jspx?nid=-34815.0.00&lc=eng&cc=US" - they tend to have more practical and theoretical information than 10 college textbooks combined.