Many problems in science and engineering have solutions that must satisfy an explicit Hamiltonian or a conservation law. The provision of computational error estimates for problems with Hamiltonians and more generally methods that are applied to a problem with an implicit conservation law is an important topic. Such problems are often solved using symplectic integrators. From this it follows that the error satisfies a differentiated form of the Hamiltonian equation. One approach that offers great promise is to use computational error tracking in which an equation for the error is explicitly integrated. Results for both ordinary and partial differential equations show that this approach works well but that care is needed in devising error tracking approaches for such problems that satisfy the appropriate conservation law.