The resistivity ${\mathrm{\ensuremath{\rho}}}_{\mathit{a}\mathit{b}}$(T) and anisotropic magnetization M(T) of ${\mathrm{ErNi}}_{2}$${\mathrm{B}}_{2}$C crystals were measured as a function of applied magnetic field (H) from 2 to 300 K to study the magnetic and superconducting properties with H parallel and perpendicular to the c axis (H\ensuremath{\parallel}c and H\ensuremath{\perp}c). Low-temperature specific-heat measurements for H=0 show a lambda-shaped anomaly associated with antiferromagnetic (AF) ordering at ${\mathit{T}}_{\mathit{N}}$=(5.85\ifmmode\pm\else\textpm\fi{}0.15) K. The ${\mathrm{\ensuremath{\rho}}}_{\mathit{a}\mathit{b}}$(T) and M(T) data show a superconducting transition at ${\mathit{T}}_{\mathit{c}}$=10.5 K, long-range AF ordering at ${\mathit{T}}_{\mathit{N}}$=6.0 K, and coexistence of superconductivity and antiferromagnetism below ${\mathit{T}}_{\mathit{N}}$. From the ${\mathrm{\ensuremath{\rho}}}_{\mathit{a}\mathit{b}}$(T) and M(T) data, the ${\mathit{T}}_{\mathit{N}}$ was found to be independent of H up to H=20 kG for H\ensuremath{\parallel}c, whereas for H\ensuremath{\perp}c ${\mathrm{T}}_{\mathit{N}}$ decreased as \ensuremath{\sim}${\mathit{H}}^{2}$ from 6.0 K at H=0 to ${\mathit{T}}_{\mathit{N}}$=3.2 K at H=18 kG. The M(T) data show a change in the easy axis direction from H\ensuremath{\parallel}c above 150 to H\ensuremath{\perp}c below 150 K. This change in anisotropy is associated with the anomalously small magnitude of the crystalline electric field ${\mathit{B}}_{2}^{0}$ term.The superconducting upper critical magnetic fields ${\mathit{H}}_{\mathit{c}2}$(T) for H\ensuremath{\parallel}c and H\ensuremath{\perp}c, determined from M(T) and ${\mathrm{\ensuremath{\rho}}}_{\mathit{a}\mathit{b}}$(H,T) data, show anomalies for both field orientations near ${\mathit{T}}_{\mathit{N}}$. However, the local minimum of ${\mathit{H}}_{\mathit{c}2}$(T) near ${\mathit{T}}_{\mathit{N}}$, seen previously for both H\ensuremath{\perp}c and H\ensuremath{\parallel}c in a ${\mathrm{HoNi}}_{2}$${\mathrm{B}}_{2}$C crystal, was found only for H\ensuremath{\parallel}c in ${\mathrm{ErNi}}_{2}$${\mathrm{B}}_{2}$C. This anisotropy in ${\mathit{H}}_{\mathit{c}2}$(T) is likely a result of the anisotropy of the Er sublattice magnetization, specifically the anisotropy of ${\mathit{T}}_{\mathit{N}}$(H). The depth of the local minimum in ${\mathit{H}}_{\mathit{c}2}$ for H\ensuremath{\parallel}c for ${\mathrm{ErNi}}_{2}$${\mathrm{B}}_{2}$C near ${\mathit{T}}_{\mathit{N}}$ is comparable to the one for ${\mathrm{HoNi}}_{2}$${\mathrm{B}}_{2}$C at 5 K.