In various geological regions, it has been postulated that the mantle lithosphere has been thinned or completely removed. Two of the primary removal mechanisms that have been put forward include: (1) delamination, a wholesale peeling away of a coherent block of the mantle lithosphere, and (2) lithospheric "dripping,'' viscous Rayleigh-Taylor instability of the mantle lithosphere. Using computational models, we investigate several near-surface observables to determine if these may be diagnostic of either (often ambiguous) removal mechanism. Surface topography associated with delamination has a broad region of uplift above the lithospheric gap and a localized and mobile zone of subsidence at the delaminating hinge. With dripping lithosphere, the topographic expression is symmetric and fixed above the downwelling. Delamination of mantle lithosphere is more efficient than dripping for thermal heating of the crust; the onset is more rapid and the elevated temperatures persist longer. The resultant crustal P-T-t paths show modest pressure variations and high temperature increases with large-scale delamination or dripping. Delamination also causes contraction directly above the (migrating) hinge and distal extension. Dripping lithosphere induces superimposed contraction and extension above and symmetric about the viscous instability. For all the observables, if only a portion of the mantle lithosphere is removed by viscous instability (delamination inherently removes all of the mantle lithosphere), the differences between the two removal mechanisms are even more pronounced. With only partial removal of the mantle lithosphere, uppermost mantle lithosphere remains well coupled to the crust, leading to lower surface temperature variations and broad zones of crustal deformation/thickening.