Yes, missiles with EM detection sensors can home in on EM signatures, and coarse-grained actives are noisy. Mostly relevant if the firing ship is destroyed, and could still be played around by an attentive player though.
I generally have fighters accompanied by sensor variants of the same size and performance , but I may also have larger and much more powerful sensor ships behind the lines.
Firepower can be made stealthy cheaply and expediently by splitting it over the smallest practical fighters.
While I typically use multiple sensor ships with one type of sensor each to reduce footprint, a large sensor can't be split up. Cloaking device and reduced-signature engines are expensive. If you care about EM signature you need to use an even larger sensor with finer resolution so the ship becomes even bigger and more expensive. All in all, I usually don't bother, and accept that my sensor ships will be quite visible. They're accompanied by a proper fleet of full-size ships AND/OR deployed far behind missile fighters that will hopefully deal with any threat without being detected themselves.
I sometimes build large, slow recon fighters or possibly FACs which can remain in space for many years. They are usually deployed in groups of 4 (R1, R50+, TH, EM), and don't really interact much with my proper military beyond checking whether a system needs my attention. The coarse Active is only turned on when needed.