Actually, I think what you're looking for is when the ebb and flood begin. For example, check out the Houston Chronicle's forecast:
Chron.com marine forecast A little over halfway down, you'll see this:
Galveston Causeway RR. bridge, Galveston, Texas Current (16d)
4/19/2012 10:31 AM CDT Max Ebb -0.44 knots
4/19/2012 1:48 PM CDT Slack, Ebb Begins -0.00 knots
4/19/2012 2:05 PM CDT Slack, Flood Begins 0.00 knots
4/19/2012 3:36 PM CDT Max Flood 0.14 knots
4/19/2012 9:02 PM CDT Max Ebb -1.36 knots
4/20/2012 1:54 AM CDT Slack, Flood Begins 0.00 knots
4/20/2012 4:55 AM CDT Max Flood 0.68 knots
4/20/2012 6:14 AM CDT Slack, Ebb Begins -0.00 knots
4/20/2012 11:30 AM CDT Max Ebb -0.43 knots
4/20/2012 1:14 PM CDT Slack, Ebb Begins -0.00 knots
4/20/2012 3:30 PM CDT Slack, Flood Begins 0.00 knots
4/20/2012 4:01 PM CDT Max Flood 0.02 knots
"Flood Begins" - Incoming Tide
"Ebb Begins" - Outgoing Tide
So, tomorrow (4/20/2012), I would expect the tide to be incoming and on the move at 1:54am. I would then expect the tide to be outgoing and on the move at 6:14am, etc. So knowing when high and low tide are helpful, but knowing when the tide will actually be moving is much more precise.
I still don't base my fishing trips on this, but I have witnessed this first hand, and these times are accurate within 5 minutes at the Galveston Causeway RR Bridge. It blew my mind the first time I actually witnessed a really strong incoming tide at the exact minute the forecast said it would happen.