I'm a fan of the model where in order to get feedback / have it affect your profile and ranking, you have to give feedback first. So whomever gives feedback first it's held in escrow until the other party does it too.

Depending on which marketplace you're talking about, but I know that Amazon doesn't want you to solicit any of their buyers since they already do it for you. On eBay, you can usually ask for feedback.

A tactic I've used is to include a reminder note within the package or packing slip that reminds the buyer how important feedback is for you and the marketplace.

I don't recommending using any software to request feedback because it's looked down upon by marketplaces is general.

Hope this helps