David, what's the context? There may be two meanings of this phrase.

l guess it was about something like this ))

How about the verb "woo" in that context?

You'll be wooed. It's ok. I didn't know this verb. What's the difference between "woo" and "court"?

Court and woo are very old fashioned words......"Run after", "pursue", and "chase" mean running after someone and replace court and woo.

Thank you! Good to know. The point is Uly Marrero translated ухаживать as "woo" on here. Looks like Americans use it though, at least, middle-aged ones. ;)

Btw, in Russian, we use similar бегать за кем-то in this sense. ;) Surprisingly, бегать за can refer both to men and women, whereas ухаживать (also a little old fashioned) is used only regarding men.