Both are now measured routinely by any medium-large pathology lab. A clinical request for fertility issues and a request for Androgens, Testosterone, Oestrogen studies, FAI, SHBG would cover all in male and female. They are measured by immunoassay on biochemistry analysers.
In the past many labs used a radio-immunoassay (RIA) for oestrogen studies that smaller labs would rather not bother with as they need access to an extra machine. RIA have been generally phased out.
No lab would use LC, MS nowadays for such a simple assay.
You need 5 ml of venous blood and fasting is not required. Interpretation needs a clinical workup and maybe a physical examination.