When I get nighttime cramps it's almost always because I'm low on magnesium in relation to calcium. Cramps during exertion are more likely to be overuse (muscle imbalance) related, both IME and from what I've read. (Eyelid tics, I'll get sometimes from low magnesium and sometimes from stress/sleep deprivation.)
I've always been a heavy sweater, but since I took up running, I just can't keep calcium, magnesium or sodium in my body without supplementing. I eat plenty of vegetables too, and I've had to increase my red meat quite a bit to get enough iron and zinc (from not eating any at all when I first started marathoning, to once or twice a week now), but when it comes to sodium and magnesium, pills and electrolyte tablets have been my friend.
If you're taking a calcium supplement single now, the first thing I'd do is to add magnesium in an equal amount.
I'm partial to Solaray brand, I take their calcium/magnesium 1:1 (can't find the product on their own site but it's easily available). Generally, capsules are going to be much more digestible than tablets, and citrates and chelates will be more bioavailable than oxides and salts - but you knew that.