Is there any way to prevent a shadow from falling on an object? I was thinking of, in particular, water surface.

Render the scene without the thing which casts the shadow or turn off the shadow casting properties of the light.

another option is to use raytraced shadows and then in the object properties turn off visible in raytracing.

An obvious option, not for purists, is to render twice, once with shadows on for the things you want to have shadows, and once without, then clone the bits you want in a 2D program.
I'm very seldom happy with my final renders as is, and the Occam's razor solution is usually preferable to hours of fussing within Poser.

Quote - another option is to use raytraced shadows and then in the object properties turn off visible in raytracing.

This one didn't work.

OK, this worked.
Step One -- make the water surface invisible and render shadows only.
Step Two -- make the water surface visible and render with no shadows.
Step Three -- composite the layers in photoshop. Put the shadow layer on top and use "multiply" to combine them.

Worked perfectly.

Sounds like your water shader isn't accurate. If you do the shader properly, it will not show a shadow anyway, even if one falls on it.

Why is that? Because you can't see water at all. You can see reflections coming from the air-water boundary (i.e. the surface), and you can see refractions of things that are in or under the water, but you can't see the water.

So a proper shader for water has no diffuse component. It is the Diffuse component that is responding to light (by making the surface brighter) or the absence of light (by making the surface darker). 

Try something like this:

Use whatever you like for bump or displacement. The important thing is that the Diffuse_Value = 0. This is the simplest possible water shader. We can get more specific features like glossy reflections of your light source too, but most people never shine a light at the right angle and direction to produce speculars anyway. But if you do need them, add a Glossy node plugged into Alternate_Specular, and adjust the parameters for small tight speculars.

PAY ATTENTION HERE:

Turn OFF the Reflection_Light_Mult and Reflection_Kd_Mult. Those parameters cause reflections to respond to light. Why? I have no freaking idea. That is what ruins the realism of reflections. They do NOT change just because light is shining or not shining on the reflection surface.