This letter investigates the design of a class of infinite-dimensional observers for one dimensional (1D) boundary controlled port-Hamiltonian systems (BC-PHS) defined by differential operators of order N ≥ 1. The convergence of the proposed observer depends on the number and location of available boundary measurements. Asymptotic convergence is assured for N≥ 1, and provided that enough boundary measurements are available, exponential convergence can be assured for the cases N=1 and N=2. Furthermore, in the case of partitioned BC-PHS with N=2, such as the Euler-Bernoulli beam, it is shown that exponential convergence can be assured considering less available measurements. The Euler-Bernoulli beam model is used to illustrate the design of the proposed observers and to perform numerical simulations.