Elastomeric adhesive compositions including a high softening point tackifier resin in combination with a base polymer can be used to create laminates having effective adhesion and elastic properties. The compositions may also include a low softening point additive, and/or an antioxidant. Facing layers, such as nonwoven webs and/or films, can be laminated to both surfaces of the elastomeric compositions to form laminates. A method of making such compositions and laminates involves forming the compositions into elastomeric adhesive films.