What makes an estimate "conservative?"

The dictionary definition of 'conservative estimate' is one which is deliberately intended to be lower than what the real value actually is.

In the case you mention, where a high estimate is the one that involves the least risk, you could reasonably argue for describing it as conservative, but you will be going against established usage and run the risk of being misunderstood. I would recommend looking for another word in this case - perhaps 'safe'.

What FF said -- a conservative estimate is the least risky, given whatever criteria for "risk" exist. As such, it may be less apt to "grab opportunity".

Eg, if I'm operating a Christmas tree lot I generally need to order all of the trees from the tree farm before the season starts, and before I have a good idea of what the market for trees will be this year. A conservative estimate of potential sales would leave my lot empty at the end of the season (lost opportunity) while a liberal estimate would leave me with unsold trees at the end (with actual money lost since I still must pay the supplier for those trees).