How do you deal with an ex?

I broke up with my ex approx 7 months ago, we’d been together just under a year (she instigated the break up – long distance relationship, struggling with lack of being able to see each other)
Shortly after we broke up i started getting calls from ‘unknown number’ (blocked) at all hours of the day and night. Caller didn’t say anything, could just hear breathing.
I had my suspicions, but didn’t know.
Weeks went by, still getting these calls. Then one night after already getting 3–4 calls from ‘unknown number’ she called – same thing, didn’t speak, just hear breathing.
Challenged her the next day – she apologised claiming she was drunk.
But this has been on going for months, and still continues.
I’ve spoken to my mobile network provider and they’ve traced calls, to… you guessed it – her phone.
Spoke to her about this – but is denying it.
I understand break ups are hard, not always easy to get over someone.
But its becoming tiresome.
I thought it she would of got bored by now.
I’m reluctant to get the police involved. As i do still care for her, and i thought it was just a phase and would ware off – but its getting beyond a joke.
Its got to the point where I’m having to take my phone off the hook each night, incase she calls, so I don’t get disturbed.
I’ve threatened her with police action; saying this is last warning, if i get another call i will go to police. But she called my bluff and calls still coming through. average 2–3 nights a week, 6–7 calls per time. hangs up seconds after i answer, and never leaves voice mail.

Apart from following through with my threat and going to the police, what else can I do?