A valve holder for delivering a prosthetic heart valve to an implant site is in various embodiments configured to reduce or eliminate the occurrence of suture looping or other damage to the prosthetic valve during implantation. The valve holder can be configured to deploy or actuate automatically when performing preparatory steps that are already familiar to practitioners, such as attaching a delivery handle to the valve holder, so that the valve holders will not require additional steps or training to use. Therefore, operation of the valve holders is kept simple, and occurrences of mistakes caused by user error can be minimized or reduced. Valve holders according to different embodiments can be designed to accommodate implantation of prosthetic heart valves from either the inflow end or the outflow end of the native valve annulus.