Keep in mind, just because a group is tax exempt (like a fraternal organization) that doesn't mean your contribution is tax deductible. Ask if it is. If so, get the group's tax ID number and make your check out to the official name of the organization, not a go-between.
Before you give, contact your local police or fire department or the police or fire union to verify whether the solicitors who approached you really are raising money for them. Try to speak to somebody other than the initial receptionist who picks up the phone.
Usually local police get all fired up about con artists using their name in vain. You can also contact your state attorney general.